2012, Rev. ed., ISBN 9780123852182, 675

Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions...

Mathematics | Functions, Zeta | Series

Mathematics | Functions, Zeta | Series

eBook

1967, Survey of recent East European mathematical literature., viii, 188

Book

2004, Mathematical Association of America, ISBN 9780521546775, x, 306

This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities....

Inequalities (Mathematics)

Inequalities (Mathematics)

Book

Applied Mathematics and Computation, ISSN 0096-3003, 01/2013, Volume 219, Issue 9, pp. 4185 - 4193

Based on the basic equations of plane and anti-plane problems and the feature of stress fields, four important properties for complex potentials expressed in power series expansion in the plane...

Power series expansion | Analytical function | Complex potentials | Basic equations | Symmetry | ELASTICITY | OPENINGS | MATHEMATICS, APPLIED | INFINITE-PLATE | FINITE | FIELD | BOUNDARY

Power series expansion | Analytical function | Complex potentials | Basic equations | Symmetry | ELASTICITY | OPENINGS | MATHEMATICS, APPLIED | INFINITE-PLATE | FINITE | FIELD | BOUNDARY

Journal Article

5.
Full Text
Closed-form calculation of infinite products of Glaisher-type related to Dirichlet series

The Ramanujan Journal, ISSN 1382-4090, 6/2019, Volume 49, Issue 2, pp. 371 - 389

... this approach in order to obtain closed-form expressions of more general infinite products which correspond to Dirichlet series...

Bendersky–Adamchik constants | Primary 40A20 | Secondary 11M06 | Fourier Analysis | Functions of a Complex Variable | Glaisher products | Field Theory and Polynomials | Infinite double products | Mathematics | Number Theory | Combinatorics | Infinite products | MATHEMATICS | Bendersky-Adamchik constants

Bendersky–Adamchik constants | Primary 40A20 | Secondary 11M06 | Fourier Analysis | Functions of a Complex Variable | Glaisher products | Field Theory and Polynomials | Infinite double products | Mathematics | Number Theory | Combinatorics | Infinite products | MATHEMATICS | Bendersky-Adamchik constants

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/2010, Volume 138, Issue 10, pp. 3393 - 3403

Recently, Bruinier, Kohnen and Ono obtained an explicit description of the action of the theta-operator on meromorphic modular forms f on SL₂(Z...

Integers | Series convergence | Mathematical theorems | Mathematical functions | Polynomials | Recurrence relations | Fourier coefficients | Mathematical cusps | Infinite products | MATHEMATICS | MATHEMATICS, APPLIED | PRODUCTS | divisors of modular forms | VALUES | Poincare series | Borcherds exponents

Integers | Series convergence | Mathematical theorems | Mathematical functions | Polynomials | Recurrence relations | Fourier coefficients | Mathematical cusps | Infinite products | MATHEMATICS | MATHEMATICS, APPLIED | PRODUCTS | divisors of modular forms | VALUES | Poincare series | Borcherds exponents

Journal Article

Modern Physics Letters B, ISSN 0217-9849, 02/2018, Volume 32, Issue 6, p. 1850082

.... By using solitary wave ansatz in the form of sech p τ function and a direct integrating way, we construct the exact bright soliton solutions and the travelling wave solutions of the equation, respectively...

bright soliton solution | explicit power series solution | A (3 + 1)-dimensional mKdV-KP equation | solitary wave ansatz | travelling wave solution | PHYSICS, CONDENSED MATTER | BREATHER WAVES | PHYSICS, APPLIED | LUMP SOLUTIONS | INFINITE CONSERVATION-LAWS | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | A (3+1)-dimensional mKdV-KP equation | NONAUTONOMOUS ROGUE WAVES | BACKLUND TRANSFORMATION | QUASI-PERIODIC WAVES | MODULATION INSTABILITY | BILINEAR EQUATIONS | RATIONAL CHARACTERISTICS

bright soliton solution | explicit power series solution | A (3 + 1)-dimensional mKdV-KP equation | solitary wave ansatz | travelling wave solution | PHYSICS, CONDENSED MATTER | BREATHER WAVES | PHYSICS, APPLIED | LUMP SOLUTIONS | INFINITE CONSERVATION-LAWS | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | A (3+1)-dimensional mKdV-KP equation | NONAUTONOMOUS ROGUE WAVES | BACKLUND TRANSFORMATION | QUASI-PERIODIC WAVES | MODULATION INSTABILITY | BILINEAR EQUATIONS | RATIONAL CHARACTERISTICS

Journal Article

Integral Transforms and Special Functions, ISSN 1065-2469, 06/2017, Volume 28, Issue 6, pp. 460 - 475

... and in the following, let and be the sets of real numbers and positive integers, respectively, and let . For the odd numbers, i.e. s=2n+1, no closed forms have been proven yet...

Riemann zeta function | Apéry's and Catalan's constant | summation formula | finite and infinite series | log-tangent integrals | Integers | Approximation | Integrals | Mathematical analysis | Transforms | Images

Riemann zeta function | Apéry's and Catalan's constant | summation formula | finite and infinite series | log-tangent integrals | Integers | Approximation | Integrals | Mathematical analysis | Transforms | Images

Journal Article

Mathematical problems in engineering, ISSN 1024-123X, 6/2018, Volume 2018, pp. 1 - 16

.... The infinite series is first summed into a very accurate, approximate closed form expression in the time domain in terms of a radical function...

MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | Random noise | Vibration | Broadband | Harmonic noise | Transfer functions | Exact solutions | Closed form solutions | Acoustics | Markov analysis | Model accuracy | Mathematical problems | Acoustic noise | State space models | Planes | Mathematical analysis | Infinite series | Ordinary differential equations | Control theory

MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | Random noise | Vibration | Broadband | Harmonic noise | Transfer functions | Exact solutions | Closed form solutions | Acoustics | Markov analysis | Model accuracy | Mathematical problems | Acoustic noise | State space models | Planes | Mathematical analysis | Infinite series | Ordinary differential equations | Control theory

Journal Article

Results in Mathematics, ISSN 1422-6383, 12/2018, Volume 73, Issue 4, pp. 1 - 18

... of trigonometric and hyperbolic functions. In particular, we evaluate in closed form certain classes of infinite series containing hyperbolic functions, which are related to Gamma functions and power of $$\pi $$ π...

hyperbolic function | 11M99 | 11M32 | Infinite series | 33B10 | Riemann zeta function | Mathematics, general | Mathematics | 11M06 | Gamma function | trigonometric function | residue theorem | MATHEMATICS | MATHEMATICS, APPLIED

hyperbolic function | 11M99 | 11M32 | Infinite series | 33B10 | Riemann zeta function | Mathematics, general | Mathematics | 11M06 | Gamma function | trigonometric function | residue theorem | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Positivity, ISSN 1385-1292, 9/2016, Volume 20, Issue 3, pp. 599 - 605

In this paper, some known results on the absolute Riesz summability factors of infinite series and Fourier series have been proved under weaker conditions...

Mathematics | Summability factor | Fourier series | Minkowski inequality | Riesz mean | 42A24 | Operator Theory | Fourier Analysis | Potential Theory | Calculus of Variations and Optimal Control; Optimization | Infinite series | 46A45 | 40G99 | Hölder inequality | Econometrics | 40F05 | 26D15 | Sequence space | 40D15 | MATHEMATICS | Holder inequality | Studies | Fourier analysis

Mathematics | Summability factor | Fourier series | Minkowski inequality | Riesz mean | 42A24 | Operator Theory | Fourier Analysis | Potential Theory | Calculus of Variations and Optimal Control; Optimization | Infinite series | 46A45 | 40G99 | Hölder inequality | Econometrics | 40F05 | 26D15 | Sequence space | 40D15 | MATHEMATICS | Holder inequality | Studies | Fourier analysis

Journal Article

National Academy Science Letters, ISSN 0250-541X, 06/2017, Volume 40, Issue 3, pp. 215 - 216

... its implications. An expansion of the Dirichlet kernel, while using a form of the Dirac delta function has been shown to yield the Taylor series in its form...

Dirac delta function | Heaviside step function | Taylor series | Dirichlet kernel | Fourier series | MULTIDISCIPLINARY SCIENCES

Dirac delta function | Heaviside step function | Taylor series | Dirichlet kernel | Fourier series | MULTIDISCIPLINARY SCIENCES

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 5/2018, Volume 46, Issue 1, pp. 91 - 102

.... This will be done by constructing generalized Dirichlet series of the form $$\sum \nolimits _{n=1}^\infty a_n n^{-s/b}$$ ∑n=1∞ann-s/b where $$b > 0$$ b>0 is an integer...

Dirichlet L -functions | Fourier Analysis | Eichler integral | 11M99 | Functions of a Complex Variable | Infinite series | Field Theory and Polynomials | Mathematics | Number Theory | Combinatorics | Mellin transform | Dirichlet L-functions | MATHEMATICS | EICHLER INTEGRALS

Dirichlet L -functions | Fourier Analysis | Eichler integral | 11M99 | Functions of a Complex Variable | Infinite series | Field Theory and Polynomials | Mathematics | Number Theory | Combinatorics | Mellin transform | Dirichlet L-functions | MATHEMATICS | EICHLER INTEGRALS

Journal Article

Educational Studies in Mathematics, ISSN 0013-1954, 10/2012, Volume 81, Issue 2, pp. 235 - 249

This is a report of a study of students' understanding of infinite series. It has a threefold purpose...

Series convergence | Mathematical sequences | Geometric series | Intervals of convergence | Infinity | Infinite series | Mathematical objects | Partial sums | Mathematical functions | Mathematics education | Limits | Conceptions | Education | APOS theory | Mathematics Education | Mathematics, general | Infinite sequence | EDUCATION & EDUCATIONAL RESEARCH | Graduate Students | Addition | Mathematical Concepts | Observation | Models | Teaching Methods | Interviews

Series convergence | Mathematical sequences | Geometric series | Intervals of convergence | Infinity | Infinite series | Mathematical objects | Partial sums | Mathematical functions | Mathematics education | Limits | Conceptions | Education | APOS theory | Mathematics Education | Mathematics, general | Infinite sequence | EDUCATION & EDUCATIONAL RESEARCH | Graduate Students | Addition | Mathematical Concepts | Observation | Models | Teaching Methods | Interviews

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 8

It is well known that the Mathieu series has a wide application in mathematics science...

Mathieu series | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | elementary method | reciprocal sums | MATHEMATICS | MATHEMATICS, APPLIED | LUCAS POLYNOMIALS | SEQUENCES | PELL NUMBERS | FIBONACCI POLYNOMIALS | INFINITE SUM | Series (mathematics) | Mathematical models | Computation | Construction methods | Inequalities | Sums | Research

Mathieu series | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | elementary method | reciprocal sums | MATHEMATICS | MATHEMATICS, APPLIED | LUCAS POLYNOMIALS | SEQUENCES | PELL NUMBERS | FIBONACCI POLYNOMIALS | INFINITE SUM | Series (mathematics) | Mathematical models | Computation | Construction methods | Inequalities | Sums | Research

Journal Article

International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, 01/2019, Volume 50, Issue 1, pp. 157 - 159

In this note we introduce an infinite series which represents an interesting challenge for students with the relevant background.

infinite series | inverse tan | Collapsing series | 97I30 | Mathematical Concepts | Mathematics | Mathematical Formulas | Fractions | Problem Solving

infinite series | inverse tan | Collapsing series | 97I30 | Mathematical Concepts | Mathematics | Mathematical Formulas | Fractions | Problem Solving

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 05/2014, Volume 366, Issue 5, pp. 2803 - 2825

In this paper we introduce the geodesic conjugacy language and geodesic conjugacy growth series for a finitely generated group...

Writing revision | Commutativity | Mathematical growth | Infinite series | Words | Rational functions | Geodesy | Mathematical functions | Direct products | Vertices | Regular languages | Conjugacy growth | Generating functions | Graph products | MATHEMATICS | generating functions | HYPERBOLIC GROUPS | graph products | regular languages

Writing revision | Commutativity | Mathematical growth | Infinite series | Words | Rational functions | Geodesy | Mathematical functions | Direct products | Vertices | Regular languages | Conjugacy growth | Generating functions | Graph products | MATHEMATICS | generating functions | HYPERBOLIC GROUPS | graph products | regular languages

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 2/2017, Volume 42, Issue 2, pp. 479 - 489

The aim of this paper is to study certain multiple series which can be regarded as multiple analogues of Eisenstein series...

Fourier Analysis | 11M41 | Multiple Eisenstein series | 11M99 | Functions of a Complex Variable | Field Theory and Polynomials | Riemann zeta function | Mathematics | Number Theory | Hyperbolic functions | Combinatorics | Lemniscate constant | MATHEMATICS

Fourier Analysis | 11M41 | Multiple Eisenstein series | 11M99 | Functions of a Complex Variable | Field Theory and Polynomials | Riemann zeta function | Mathematics | Number Theory | Hyperbolic functions | Combinatorics | Lemniscate constant | MATHEMATICS

Journal Article

Electronic Journal of Combinatorics, ISSN 1077-8926, 03/2015, Volume 22, Issue 1, p. 1.59

We evaluate in closed form series of the type Sigma u(n)R(n), with (u(n))(n), a strongly B-multiplicative sequence and R(n) a (well-chosen) rational function...

Summation of series | Golay-shapiro-rudin sequence | Strongly B-multiplicative sequences | Paperfolding sequence | COUNTING BLOCKS | MATHEMATICS | MATHEMATICS, APPLIED | strongly B-multiplicative sequences | Golay-Shapiro-Rudin sequence | paperfolding sequence | INFINITE PRODUCTS | DIGITS | summation of series | Mathematics

Summation of series | Golay-shapiro-rudin sequence | Strongly B-multiplicative sequences | Paperfolding sequence | COUNTING BLOCKS | MATHEMATICS | MATHEMATICS, APPLIED | strongly B-multiplicative sequences | Golay-Shapiro-Rudin sequence | paperfolding sequence | INFINITE PRODUCTS | DIGITS | summation of series | Mathematics

Journal Article

1975, Prentice-Hall series in automatic computation, ISBN 0138819386, xviii, 523

Book

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