Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2015, Volume 429, Issue 2, pp. 744 - 757

...) is the Ramanujan constant function. Besides, as the key tool, the series expression for the Ramanujan constant function R(x) is given.

Ramanujan constant function | Gaussian hypergeometric function | Generalized elliptic integral | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | MODULAR EQUATIONS

Ramanujan constant function | Gaussian hypergeometric function | Generalized elliptic integral | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | MODULAR EQUATIONS

Journal Article

Mathematical Notes, ISSN 0001-4346, 10/2010, Volume 88, Issue 3, pp. 599 - 602

A new supercongruence associated with a Gaussian hypergeometric series, as well as one...

elliptic curve | supercongruence | ramified double cover | finite field | Mathematics, general | Mathematics | Hasse invariant | Legendre transform | MATHEMATICS | GAUSSIAN HYPERGEOMETRIC-SERIES

elliptic curve | supercongruence | ramified double cover | finite field | Mathematics, general | Mathematics | Hasse invariant | Legendre transform | MATHEMATICS | GAUSSIAN HYPERGEOMETRIC-SERIES

Journal Article

Journal of Applied Mathematics and Stochastic Analysis, ISSN 1048-9533, 1995, Volume 8, Issue 2, pp. 189 - 194

Journal Article

84.
Full Text
Outage probability of MRC for κ-μ shadowed fading channels under co-channel interference

PLoS ONE, ISSN 1932-6203, 11/2016, Volume 11, Issue 11, p. e0166528

...) and background white Gaussian noise. To this end, first, the probability density function (PDF) of the κ-μ shadowed fading distribution is obtained in the form of a power series...

Models, Theoretical | Probability | Algorithms | Computer Simulation | Signal-To-Noise Ratio | Wireless Technology | Performance evaluation | Random noise | Laboratories | Noise | Cochannel interference | Gaussian distribution | Background noise | Power series | Channels | Probability density functions | Wireless communications | Mathematical analysis | Receivers & amplifiers | Computer networks | Background radiation | Fading | Immunoglobulins | Statistical analysis | Computer simulation | Interference | Exact solutions | Closed form solutions | Supercomputers | Computer science | Communications systems | Wireless communication systems | Communication channels

Models, Theoretical | Probability | Algorithms | Computer Simulation | Signal-To-Noise Ratio | Wireless Technology | Performance evaluation | Random noise | Laboratories | Noise | Cochannel interference | Gaussian distribution | Background noise | Power series | Channels | Probability density functions | Wireless communications | Mathematical analysis | Receivers & amplifiers | Computer networks | Background radiation | Fading | Immunoglobulins | Statistical analysis | Computer simulation | Interference | Exact solutions | Closed form solutions | Supercomputers | Computer science | Communications systems | Wireless communication systems | Communication channels

Journal Article

IEEE Transactions on Communications, ISSN 0090-6778, 07/2007, Volume 55, Issue 7, pp. 1407 - 1416

...) of the sum of Nakagami- m random variables. Exact infinite series representations are derived for the sum of three and four identically and independently distributed (i.i.d...

Fading | Fourier transforms | Rayleigh channels | Performance gain | Rayleigh density | probability density function (pdf) | Characteristic function (chf) | Nakagami distribution | diversity | Nakagami- m distribution | Diversity reception | equal gain combining (EGC) receiver | Gaussian processes | Probability density function | Random variables | Performance analysis | Probability density function (pdf) | Diversity | Nakagami-m distribution | Equal gain combining (EGC) receiver | INFINITE SERIES | RAYLEIGH | PERFORMANCE | TELECOMMUNICATIONS | fading | characteristic function (chf) | ENGINEERING, ELECTRICAL & ELECTRONIC | PROBABILITY | EQUAL-GAIN DIVERSITY | CHANNELS | Signal processing | Methods

Fading | Fourier transforms | Rayleigh channels | Performance gain | Rayleigh density | probability density function (pdf) | Characteristic function (chf) | Nakagami distribution | diversity | Nakagami- m distribution | Diversity reception | equal gain combining (EGC) receiver | Gaussian processes | Probability density function | Random variables | Performance analysis | Probability density function (pdf) | Diversity | Nakagami-m distribution | Equal gain combining (EGC) receiver | INFINITE SERIES | RAYLEIGH | PERFORMANCE | TELECOMMUNICATIONS | fading | characteristic function (chf) | ENGINEERING, ELECTRICAL & ELECTRONIC | PROBABILITY | EQUAL-GAIN DIVERSITY | CHANNELS | Signal processing | Methods

Journal Article

IEEE Signal Processing Letters, ISSN 1070-9908, 11/2007, Volume 14, Issue 11, pp. 864 - 866

Performance analysis of the normalized adaptive matched filter (NAMF) operating in homogeneous Gaussian clutter has received considerable attention in the...

CPU time | exponential integral | Appell hypergeometric series of the first kind | probability of false alarm | complementary incomplete gamma function | compound-Gaussian clutter | probability of detection | Matched filters | Gamma ray detectors | Integral equations | incomplete beta function | Object detection | Gamma ray detection | Probability of false alarm | Complementary incomplete gamma function | Compound-Gaussian clutter | Incomplete beta function | Exponential integral | Probability of detection | PERFORMANCE | appell hypergeometric series of the first kind | STAP TESTS | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Gaussian | Clutter | False alarms

CPU time | exponential integral | Appell hypergeometric series of the first kind | probability of false alarm | complementary incomplete gamma function | compound-Gaussian clutter | probability of detection | Matched filters | Gamma ray detectors | Integral equations | incomplete beta function | Object detection | Gamma ray detection | Probability of false alarm | Complementary incomplete gamma function | Compound-Gaussian clutter | Incomplete beta function | Exponential integral | Probability of detection | PERFORMANCE | appell hypergeometric series of the first kind | STAP TESTS | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Gaussian | Clutter | False alarms

Journal Article

Integral Transforms and Special Functions, ISSN 1065-2469, 06/2001, Volume 11, Issue 3, pp. 233 - 256

The extended hypergeometric equation is a generalization of the Gaussian hypergeometric equation (Section 1...

asymptotic expansions for extended hypergeometric equation | Frobenius-Fuchs method | Mathieu functions | Laurent series | mean flow | Gaussian and generalized hypergeometric equations | Mach number | Asymptotic expansions for extended hypergeometric equation | Mean flow | GASES | MATHEMATICS, APPLIED | Mathieu funcions | MAGNETO-ATMOSPHERIC WAVES | GRAVITY-WAVES | FIELD | HYDROMAGNETIC-WAVES | MATHEMATICS | MODES | ALFVEN WAVES | SOUND | OSCILLATIONS | PROPAGATION

asymptotic expansions for extended hypergeometric equation | Frobenius-Fuchs method | Mathieu functions | Laurent series | mean flow | Gaussian and generalized hypergeometric equations | Mach number | Asymptotic expansions for extended hypergeometric equation | Mean flow | GASES | MATHEMATICS, APPLIED | Mathieu funcions | MAGNETO-ATMOSPHERIC WAVES | GRAVITY-WAVES | FIELD | HYDROMAGNETIC-WAVES | MATHEMATICS | MODES | ALFVEN WAVES | SOUND | OSCILLATIONS | PROPAGATION

Journal Article

Statistical Inference for Stochastic Processes, ISSN 1387-0874, 4/2017, Volume 20, Issue 1, pp. 79 - 103

In this paper, we study the memory properties of transformations of linear processes. Dittmann and Granger (J Econ 110:113–133, 2002) studied the polynomial...

Short memory | 62M10 | Linear process | Heavy tail | Nonlinear transformation | 62E20 | Probability Theory and Stochastic Processes | Non-stationary | Mathematics | Long memory | Analysis | Memory | Information management

Short memory | 62M10 | Linear process | Heavy tail | Nonlinear transformation | 62E20 | Probability Theory and Stochastic Processes | Non-stationary | Mathematics | Long memory | Analysis | Memory | Information management

Journal Article

Multidimensional Systems and Signal Processing, ISSN 0923-6082, 10/2018, Volume 29, Issue 4, pp. 1553 - 1561

...y,σy2) . The derived joint probability distribution only contains a confluent hypergeometric function of the first kind $${_1F_{1...

Engineering | Signal,Image and Speech Processing | Complex Gaussian random variable | Artificial Intelligence (incl. Robotics) | Circuits and Systems | Ratio distribution | Rice distribution | Electrical Engineering | COMPUTER SCIENCE, THEORY & METHODS | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Robotics | Gaussian processes

Engineering | Signal,Image and Speech Processing | Complex Gaussian random variable | Artificial Intelligence (incl. Robotics) | Circuits and Systems | Ratio distribution | Rice distribution | Electrical Engineering | COMPUTER SCIENCE, THEORY & METHODS | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Robotics | Gaussian processes

Journal Article

The Annals of Probability, ISSN 0091-1798, 1/1997, Volume 25, Issue 1, pp. 457 - 477

In this paper we prove central limit theorems of the following kind: let be the unit sphere of dimension d ≥ 2 with uniform distribution ω . For each k∈N,...

Hypergeometric functions | Transition probabilities | Haar measures | Central limit theorem | Random walk | Markov chains | Fourier transformations | Perceptron convergence procedure | Borel sets | Jacobi polynomials | Compact symmetric spaces of rank one | Gaussian measures | Random walks on n-spheres | Total variation distance | central limit theorem | SERIES | RANDOM-WALKS | SPACES | STATISTICS & PROBABILITY | POSITIVITY | CONVOLUTION | random walks on n-spheres | compact symmetric spaces of rank one | total variation distance | 33C25 | 42C10 | 60B10 | 43A62 | 60J15 | 60F05

Hypergeometric functions | Transition probabilities | Haar measures | Central limit theorem | Random walk | Markov chains | Fourier transformations | Perceptron convergence procedure | Borel sets | Jacobi polynomials | Compact symmetric spaces of rank one | Gaussian measures | Random walks on n-spheres | Total variation distance | central limit theorem | SERIES | RANDOM-WALKS | SPACES | STATISTICS & PROBABILITY | POSITIVITY | CONVOLUTION | random walks on n-spheres | compact symmetric spaces of rank one | total variation distance | 33C25 | 42C10 | 60B10 | 43A62 | 60J15 | 60F05

Journal Article

Advances in mathematical physics, ISSN 1687-9120, 10/2013, Volume 2013, pp. 1 - 3

...1. Introduction LRD time series increasingly gains applications to many fields of science and technologies; see, for example, Mandelbrot [1] and references...

PHYSICS, MATHEMATICAL | Functions (mathematics) | Autocorrelation functions | Noise | Mathematical analysis | Gaussian | Density | Standards

PHYSICS, MATHEMATICAL | Functions (mathematics) | Autocorrelation functions | Noise | Mathematical analysis | Gaussian | Density | Standards

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 02/2011, Volume 217, Issue 12, pp. 5702 - 5728

...–Bernoulli polynomials and the Apostol–Euler polynomials, and derive various explicit series representations in terms of the Gaussian hypergeometric function and the Hurwitz (or generalized) zeta function...

Lerch’s functional equation | Hurwitz (or generalized), Hurwitz–Lerch and Lipschitz–Lerch zeta functions | Srivastava’s formula and Gaussian hypergeometric function | Genocchi numbers and Genocchi polynomials of higher order | Stirling numbers and the λ-Stirling numbers of the second kind | Apostol–Genocchi numbers and Apostol–Genocchi polynomials of higher order | Apostol–Bernoulli polynomials and Apostol–Euler polynomials of higher order | Apostol–Genocchi numbers and Apostol–Genocchi polynomials | Apostol-Bernoulli polynomials and Apostol-Euler polynomials of higher order | Srivastava's formula and Gaussian hypergeometric function | Hurwitz (or generalized), Hurwitz-Lerch and Lipschitz-Lerch zeta functions | Apostol-Genocchi numbers and Apostol-Genocchi polynomials | Apostol-Genocchi numbers and Apostol-Genocchi polynomials of higher order | Lerch's functional equation | FOURIER EXPANSIONS | MATHEMATICS, APPLIED | IDENTITIES | Q-EXTENSIONS | BERNOULLI | EXPLICIT FORMULA | ORDER | Stirling numbers and the lambda-Stirling numbers of the second kind | EULER POLYNOMIALS | INTEGRAL-REPRESENTATIONS | Hypergeometric functions | Analogue | Computation | Mathematical analysis | Gaussian | Mathematical models | Error correction | Representations

Lerch’s functional equation | Hurwitz (or generalized), Hurwitz–Lerch and Lipschitz–Lerch zeta functions | Srivastava’s formula and Gaussian hypergeometric function | Genocchi numbers and Genocchi polynomials of higher order | Stirling numbers and the λ-Stirling numbers of the second kind | Apostol–Genocchi numbers and Apostol–Genocchi polynomials of higher order | Apostol–Bernoulli polynomials and Apostol–Euler polynomials of higher order | Apostol–Genocchi numbers and Apostol–Genocchi polynomials | Apostol-Bernoulli polynomials and Apostol-Euler polynomials of higher order | Srivastava's formula and Gaussian hypergeometric function | Hurwitz (or generalized), Hurwitz-Lerch and Lipschitz-Lerch zeta functions | Apostol-Genocchi numbers and Apostol-Genocchi polynomials | Apostol-Genocchi numbers and Apostol-Genocchi polynomials of higher order | Lerch's functional equation | FOURIER EXPANSIONS | MATHEMATICS, APPLIED | IDENTITIES | Q-EXTENSIONS | BERNOULLI | EXPLICIT FORMULA | ORDER | Stirling numbers and the lambda-Stirling numbers of the second kind | EULER POLYNOMIALS | INTEGRAL-REPRESENTATIONS | Hypergeometric functions | Analogue | Computation | Mathematical analysis | Gaussian | Mathematical models | Error correction | Representations

Journal Article

Discrete Mathematics, ISSN 0012-365X, 2005, Volume 300, Issue 1, pp. 44 - 56

We define two finite q-analogs of certain multiple harmonic series with an arbitrary number of free parameters, and prove identities for these q-analogs, expressing them in terms of multiply nested...

Multiple zeta values | Duality | q-series | Finite q-analog | Multiple harmonic series | Gaussian binomial coefficients | MATHEMATICS | ZETA-VALUES | IDENTITIES | multiple zeta values | ALGEBRA | finite q-analog | multiple harmonic series | duality | COMBINATORICS

Multiple zeta values | Duality | q-series | Finite q-analog | Multiple harmonic series | Gaussian binomial coefficients | MATHEMATICS | ZETA-VALUES | IDENTITIES | multiple zeta values | ALGEBRA | finite q-analog | multiple harmonic series | duality | COMBINATORICS

Journal Article

94.
Full Text
New class of generating functions associated with generalized hypergeometric polynomials

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2003, Volume 285, Issue 2, pp. 642 - 650

... generalized hypergeometric polynomials and multiple hypergeometric series of several variables...

Pochhammer symbol | Bounded multiple sequence | Generating function | Hypergeometric polynomials | Multiple Gaussian hypergeometric functions | MATHEMATICS | MATHEMATICS, APPLIED | pochhammer symbol | hypergeometric polynomials | generating function | bounded multiple sequence | multiple Gaussian hypergeometric functions

Pochhammer symbol | Bounded multiple sequence | Generating function | Hypergeometric polynomials | Multiple Gaussian hypergeometric functions | MATHEMATICS | MATHEMATICS, APPLIED | pochhammer symbol | hypergeometric polynomials | generating function | bounded multiple sequence | multiple Gaussian hypergeometric functions

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 03/2012, Volume 81, Issue 278, pp. 861 - 877

The problem of the rate of convergence of Legendre approximation is considered. We first establish the decay rates of the coefficients in the Legendre series...

Interpolation | Numerical quadratures | Approximation | Series expansion | Error bounds | Polynomials | Coefficients | Legendre polynomials | Gaussian quadratures | Spectral methods | Barycentric Lagrange interpolation | Legendre expansion | Chebyshev expansion | Bernstein ellipse | barycentric Lagrange interpolation | INTERPOLATION | MATHEMATICS, APPLIED | SPECTRAL-GALERKIN METHOD | 2ND-ORDER | GAUSS QUADRATURE | DIRECT SOLVERS | FAST ALGORITHM

Interpolation | Numerical quadratures | Approximation | Series expansion | Error bounds | Polynomials | Coefficients | Legendre polynomials | Gaussian quadratures | Spectral methods | Barycentric Lagrange interpolation | Legendre expansion | Chebyshev expansion | Bernstein ellipse | barycentric Lagrange interpolation | INTERPOLATION | MATHEMATICS, APPLIED | SPECTRAL-GALERKIN METHOD | 2ND-ORDER | GAUSS QUADRATURE | DIRECT SOLVERS | FAST ALGORITHM

Journal Article

Integral transforms and special functions, ISSN 1476-8291, 2019, Volume 30, Issue 5, pp. 418 - 430

.... The associated crossed term integral is investigated and solved by introducing a computational series built from hypergeometric-type terms for different values of parameters involved...

Kampé de Fériet hypergeometric function of two variables | generalized hypergeometric function | closed form | Bessel function of the first kind | Gaussian hypergeometric function | integral form | Appell function | DENSITY | MATHEMATICS | Kampe de Feriet hypergeometric function of two variables | MATHEMATICS, APPLIED | THIN STRAIGHT WIRE | Mathematical models | Cylinders

Kampé de Fériet hypergeometric function of two variables | generalized hypergeometric function | closed form | Bessel function of the first kind | Gaussian hypergeometric function | integral form | Appell function | DENSITY | MATHEMATICS | Kampe de Feriet hypergeometric function of two variables | MATHEMATICS, APPLIED | THIN STRAIGHT WIRE | Mathematical models | Cylinders

Journal Article

Annales Polonici Mathematici, ISSN 0066-2216, 2015, Volume 113, Issue 1, pp. 93 - 108

.... We obtain conditions on the coefficients of power series of functions analytic in the unit disk which ensure that they generate functions in the q-close-to-convex family...

Univalent analytic functions | Q-starlike and q-close-to-convex functions | Special functions | Bieberbach–de branges theorem | Q-difference operator | Starlike and close-to-convex functions | MATHEMATICS | STARLIKENESS | ORDER | univalent analytic functions | Bieberbach de Branges theorem | GAUSSIAN HYPERGEOMETRIC-FUNCTIONS | UNIVALENCE | starlike and close-to-convex functions | q-starlike and q-close-to-convex functions | q-difference operator | special functions

Univalent analytic functions | Q-starlike and q-close-to-convex functions | Special functions | Bieberbach–de branges theorem | Q-difference operator | Starlike and close-to-convex functions | MATHEMATICS | STARLIKENESS | ORDER | univalent analytic functions | Bieberbach de Branges theorem | GAUSSIAN HYPERGEOMETRIC-FUNCTIONS | UNIVALENCE | starlike and close-to-convex functions | q-starlike and q-close-to-convex functions | q-difference operator | special functions

Journal Article

Fractal and Fractional, ISSN 2504-3110, 12/2017, Volume 1, Issue 1, p. 16

.... The special functions are obtained from the series solution of these equations. We study different properties of these special functions and establish the relation with other functions...

Ordinary differential equations | Researchers | Pantographs | Industrial research | Gaussian binomial coefficient | fractional derivative | pantograph equation | proportional delay

Ordinary differential equations | Researchers | Pantographs | Industrial research | Gaussian binomial coefficient | fractional derivative | pantograph equation | proportional delay

Journal Article

1973, AD-a425 952.

.... Two of these expressions take the form of an infinite series involving either confluent hypergeometric functions or modified Bessel functions...

infinite series | bessel functions | uplinks | transmitter receivers | demodulation | downlinks | gaussian noise | hypergeometric functions | cross correlation | channels | communication and radio systems | phase shift keyers | repeaters

infinite series | bessel functions | uplinks | transmitter receivers | demodulation | downlinks | gaussian noise | hypergeometric functions | cross correlation | channels | communication and radio systems | phase shift keyers | repeaters

Government Document

IEEE Transactions on Signal Processing, ISSN 1053-587X, 11/2012, Volume 60, Issue 11, pp. 6053 - 6058

Using only the phase information and a relationship based on the Gaussian Hypergeometric function, the Phase-Phase Correlator can be utilized to estimate the normalized cross-correlation coefficient...

Maximum likelihood estimation | Correlation | Noise | Correlators | phase-phase correlator | Random processes | outliers | Bias curve | Contamination | Robustness | impulsive noise | correlation coefficient | robust statistics | MULTICARRIER | ESTIMATOR | ENGINEERING, ELECTRICAL & ELECTRONIC | Robust statistics | Usage | Maximum likelihood estimates (Statistics) | Analysis | Transfer functions | Gaussian processes | Innovations | Signal processing | Asymptotic properties | Time series analysis | Gaussian | Estimates | Automotive engineering

Maximum likelihood estimation | Correlation | Noise | Correlators | phase-phase correlator | Random processes | outliers | Bias curve | Contamination | Robustness | impulsive noise | correlation coefficient | robust statistics | MULTICARRIER | ESTIMATOR | ENGINEERING, ELECTRICAL & ELECTRONIC | Robust statistics | Usage | Maximum likelihood estimates (Statistics) | Analysis | Transfer functions | Gaussian processes | Innovations | Signal processing | Asymptotic properties | Time series analysis | Gaussian | Estimates | Automotive engineering

Journal Article

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