Filomat, ISSN 0354-5180, 1/2016, Volume 30, Issue 7, pp. 1957 - 1967

In this paper, we obtain a new identity using the partial fraction decomposition...

Binomials | Partial fraction decomposition | Grants | Extension | Binomial identity | MATHEMATICS | MATHEMATICS, APPLIED | extension | partial fraction decomposition | HARMONIC NUMBERS | FORMULAS | SUMS

Binomials | Partial fraction decomposition | Grants | Extension | Binomial identity | MATHEMATICS | MATHEMATICS, APPLIED | extension | partial fraction decomposition | HARMONIC NUMBERS | FORMULAS | SUMS

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 12/2015, Volume 38, Issue 3, pp. 455 - 463

... based on the partial fraction decomposition, and use them to determine a basis for the space of modular forms of weight $$k$$ k on $$\mathrm{SL}_2 ({\mathbb Z})$$ SL...

Fourier Analysis | Functions of a Complex Variable | Partial fraction decomposition | Field Theory and Polynomials | Eisenstein series | MSC 11F67 | Mathematics | Number Theory | Combinatorics | MSC 11F11 | FORMS | MATHEMATICS

Fourier Analysis | Functions of a Complex Variable | Partial fraction decomposition | Field Theory and Polynomials | Eisenstein series | MSC 11F67 | Mathematics | Number Theory | Combinatorics | MSC 11F11 | FORMS | MATHEMATICS

Journal Article

Chemical Physics, ISSN 0301-0104, 2010, Volume 370, Issue 1, pp. 109 - 114

We implement the partial fraction decomposition scheme proposed by Croy and Saalmann [A. Croy, U. Saalmann, Phys. Rev. B 80 (2009) 073102...

Quantum dissipation | Bose–Einstein function | Hierarchical equations of motion | Partial fraction decomposition | Bose-Einstein function | SYSTEM | NOISE BATH | TEMPERATURE | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | DYNAMICS | CHEMISTRY, PHYSICAL | TIME | INITIAL-VALUE REPRESENTATION | Physics - Statistical Mechanics

Quantum dissipation | Bose–Einstein function | Hierarchical equations of motion | Partial fraction decomposition | Bose-Einstein function | SYSTEM | NOISE BATH | TEMPERATURE | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | DYNAMICS | CHEMISTRY, PHYSICAL | TIME | INITIAL-VALUE REPRESENTATION | Physics - Statistical Mechanics

Journal Article

Forum Mathematicum, ISSN 0933-7741, 03/2015, Volume 27, Issue 2, pp. 735 - 766

We provide new formulas for the coefficients in the partial fraction decomposition of the restricted partition generating function...

partial fraction decomposition | Bernoulli polynomial | 11P82 | Sylvester wave | 11B68 | Restricted partition | MATHEMATICS | MATHEMATICS, APPLIED | SERIES

partial fraction decomposition | Bernoulli polynomial | 11P82 | Sylvester wave | 11B68 | Restricted partition | MATHEMATICS | MATHEMATICS, APPLIED | SERIES

Journal Article

Applicable Algebra in Engineering, Communication and Computing, ISSN 0938-1279, 11/2015, Volume 26, Issue 5, pp. 427 - 463

...AAECC (2015) 26:427–463 DOI 10.1007/s00200-015-0256-5 ORIGINAL PAPER On sequences, rational functions and decomposition Graham H. Norton 1 Received: 5 December...

Laurent series | Theory of Computation | Linear recurrence | Minimal polynomial | Continued fraction | Partial quotient | Computer Hardware | Berlekamp–Massey algorithm | Computer Science | Artificial Intelligence (incl. Robotics) | Key equation | Symbolic and Algebraic Manipulation | Rational function | MATHEMATICS, APPLIED | Berlekamp-Massey algorithm | SHIFT-REGISTER SYNTHESIS | ALGORITHM | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTER SCIENCE, THEORY & METHODS | CONTINUED FRACTIONS | Algorithms | Computer Science - Symbolic Computation

Laurent series | Theory of Computation | Linear recurrence | Minimal polynomial | Continued fraction | Partial quotient | Computer Hardware | Berlekamp–Massey algorithm | Computer Science | Artificial Intelligence (incl. Robotics) | Key equation | Symbolic and Algebraic Manipulation | Rational function | MATHEMATICS, APPLIED | Berlekamp-Massey algorithm | SHIFT-REGISTER SYNTHESIS | ALGORITHM | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTER SCIENCE, THEORY & METHODS | CONTINUED FRACTIONS | Algorithms | Computer Science - Symbolic Computation

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2008, Volume 136, Issue 1, pp. 229 - 237

The partial fraction decomposition method is explored to establish several interesting trigonometric function identities, which may have applications to the evaluation of classical multiple...

Complex numbers | Interpolation | Partial fractions | Applied mathematics | Natural numbers | Partial fraction decomposition | Sine function | Polynomials | Cots | Trigonometric identities | MATHEMATICS | MATHEMATICS, APPLIED | partial fraction decomposition | trigonometric interpolation | THEOREMS | trigonometric formulae

Complex numbers | Interpolation | Partial fractions | Applied mathematics | Natural numbers | Partial fraction decomposition | Sine function | Polynomials | Cots | Trigonometric identities | MATHEMATICS | MATHEMATICS, APPLIED | partial fraction decomposition | trigonometric interpolation | THEOREMS | trigonometric formulae

Journal Article

IEEE Transactions on Circuits and Systems II: Express Briefs, ISSN 1549-7747, 08/2019, Volume 66, Issue 8, pp. 1461 - 1465

In this brief, we consider the minimax design of infinite impulse response (IIR) filter. First, we apply the partial fraction method to decompose the transfer...

minimax design | Circuits and systems | Stability criteria | IIR digital filter | Transfer functions | partial fraction decomposition | Circuit stability | Optimization | Numerical stability | DIGITAL-FILTERS | PRESCRIBED MAGNITUDE | ENGINEERING, ELECTRICAL & ELECTRONIC

minimax design | Circuits and systems | Stability criteria | IIR digital filter | Transfer functions | partial fraction decomposition | Circuit stability | Optimization | Numerical stability | DIGITAL-FILTERS | PRESCRIBED MAGNITUDE | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Journal of Lightwave Technology, ISSN 0733-8724, 01/2000, Volume 18, Issue 1, pp. 50 - 56

We develop a modal decomposition approach to solve the full vector wave equation for holey optical fibers (HF...

Optical fibers | Photonic band gap | Partial differential equations | Refractive index | Lattices | Hafnium | Optical fiber devices | Optical refraction | Periodic structures | Optical fiber dispersion | eigenfunctions | eigenvalues | optical fiber applications | periodic structures | modeling | optical dispersion | orthogonal function methods | PHOTONIC CRYSTAL FIBER | OPTICS | ENGINEERING, ELECTRICAL & ELECTRONIC | Decomposition | Flexibility | Optical properties | Wave equations

Optical fibers | Photonic band gap | Partial differential equations | Refractive index | Lattices | Hafnium | Optical fiber devices | Optical refraction | Periodic structures | Optical fiber dispersion | eigenfunctions | eigenvalues | optical fiber applications | periodic structures | modeling | optical dispersion | orthogonal function methods | PHOTONIC CRYSTAL FIBER | OPTICS | ENGINEERING, ELECTRICAL & ELECTRONIC | Decomposition | Flexibility | Optical properties | Wave equations

Journal Article

Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 4/2008, Volume 2, Issue 1, pp. 65 - 68

.... Appl. Anal. Discrete Math., 1 (2007), 397-402, are treated by inverting them; the resulting sums are evaluated using partial fraction decomposition, following Wenchang Chu...

Discrete mathematics | Partial fraction decomposition | Identity | Partial fractions decomposition | Inverse pairs | MATHEMATICS | MATHEMATICS, APPLIED | decomposition | inverse pairs | partial fractions

Discrete mathematics | Partial fraction decomposition | Identity | Partial fractions decomposition | Inverse pairs | MATHEMATICS | MATHEMATICS, APPLIED | decomposition | inverse pairs | partial fractions

Journal Article

KUWAIT JOURNAL OF SCIENCE, ISSN 2307-4108, 01/2020, Volume 47, Issue 1, pp. 14 - 21

.... Our approach uses the elementary technique of partial fraction decomposition. Furthermore, some of the sums, which he studied in 2017, are treated in the same style.

MULTIDISCIPLINARY SCIENCES | Partial fraction decomposition | reciprocal sum identities | trigonometric functions

MULTIDISCIPLINARY SCIENCES | Partial fraction decomposition | reciprocal sum identities | trigonometric functions

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2007, Volume 207, Issue 2, pp. 331 - 337

We find convergent double series expansions for Legendre's third incomplete elliptic integral valid in overlapping subdomains of the unit square. Truncated...

Series expansion | Asymptotic approximation | Incomplete elliptic integral | Partial fraction decomposition | MATHEMATICS, APPLIED | partial fraction decomposition | series expansion | incomplete elliptic integral | ASYMPTOTIC EXPANSIONS | asymptotic approximation | Mathematics - Classical Analysis and ODEs

Series expansion | Asymptotic approximation | Incomplete elliptic integral | Partial fraction decomposition | MATHEMATICS, APPLIED | partial fraction decomposition | series expansion | incomplete elliptic integral | ASYMPTOTIC EXPANSIONS | asymptotic approximation | Mathematics - Classical Analysis and ODEs

Journal Article

The College Mathematics Journal, ISSN 0746-8342, 3/2006, Volume 37, Issue 2, pp. 132 - 134

Journal Article

13.
Full Text
Asymptotics for the partial fractions of the restricted partition generating function I

International Journal of Number Theory, ISSN 1793-0421, 09/2016, Volume 12, Issue 6, pp. 1421 - 1474

.... We find the behavior of coefficients in the partial fraction decomposition of this product as N...

partial fraction decomposition | saddle-point method | Restricted partitions | dilogarithm | MATHEMATICS | CONJECTURE

partial fraction decomposition | saddle-point method | Restricted partitions | dilogarithm | MATHEMATICS | CONJECTURE

Journal Article

Magnetic Resonance in Medicine, ISSN 0740-3194, 06/2018, Volume 79, Issue 6, pp. 2886 - 2895

.... Methods A spectral decomposition (sDec) technique was evaluated for separation of spectra from white matter (WM) and gray matter (GM...

spectral decomposition | partial volume effects | white matter | MR spectroscopic imaging (MRSI) | gray matter | LOCALIZATION | HUMAN BRAIN | DISTRIBUTIONS | MAGNETIC-RESONANCE-SPECTROSCOPY | THALAMUS | CLINICAL-APPLICATIONS | METABOLIC-CHANGES | IN-VIVO | SEGMENTATION | SEPARATION | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Brain - diagnostic imaging | Reproducibility of Results | Magnetic Resonance Spectroscopy | Humans | Middle Aged | Signal-To-Noise Ratio | Linear Models | Male | Gray Matter - diagnostic imaging | Tissue Distribution | White Matter - diagnostic imaging | Algorithms | Computer Simulation | Brain Mapping | Adult | Female | Cohort Studies | Medicine, Experimental | Medical research | Brain research | Metabolites | Image processing | Neuroimaging | Brain | Data processing | Decomposition | Spectra | Regression analysis | Tissues | Substantia alba | Putamen | Substantia grisea | Spectral analysis | Magnetic resonance imaging | Simulation | In vivo methods and tests | magnetic resonance spectroscopic imaging (MRSI) | gray-matter | white-matter

spectral decomposition | partial volume effects | white matter | MR spectroscopic imaging (MRSI) | gray matter | LOCALIZATION | HUMAN BRAIN | DISTRIBUTIONS | MAGNETIC-RESONANCE-SPECTROSCOPY | THALAMUS | CLINICAL-APPLICATIONS | METABOLIC-CHANGES | IN-VIVO | SEGMENTATION | SEPARATION | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Brain - diagnostic imaging | Reproducibility of Results | Magnetic Resonance Spectroscopy | Humans | Middle Aged | Signal-To-Noise Ratio | Linear Models | Male | Gray Matter - diagnostic imaging | Tissue Distribution | White Matter - diagnostic imaging | Algorithms | Computer Simulation | Brain Mapping | Adult | Female | Cohort Studies | Medicine, Experimental | Medical research | Brain research | Metabolites | Image processing | Neuroimaging | Brain | Data processing | Decomposition | Spectra | Regression analysis | Tissues | Substantia alba | Putamen | Substantia grisea | Spectral analysis | Magnetic resonance imaging | Simulation | In vivo methods and tests | magnetic resonance spectroscopic imaging (MRSI) | gray-matter | white-matter

Journal Article

Turkish Journal of Mathematics, ISSN 1300-0098, 2018, Volume 42, Issue 1, pp. 307 - 311

A class of double sums with binomial coefficients are evaluated by combining finite differences with partial fraction decompositions.

Finite difference | Binomial coefficient | Telescoping method | Partial fraction decomposition | MATHEMATICS | partial fraction decomposition | telescoping method | IDENTITIES | finite difference

Finite difference | Binomial coefficient | Telescoping method | Partial fraction decomposition | MATHEMATICS | partial fraction decomposition | telescoping method | IDENTITIES | finite difference

Journal Article

Journal of Engineering Mechanics, ISSN 0733-9399, 08/2016, Volume 142, Issue 8, pp. 1 - 10

AbstractSystems of second-order linear ordinary differential equations (ODEs) to arbitrary input functions appear in many fields of physics and engineering....

Technical Papers | Laplace transform | Residue | Dynamic analysis | Pole | Partial fraction expansion | DECOMPOSITION | ENGINEERING, MECHANICAL | Mechanics | Usage | Laplace transformation | Research | Differential equations | Tests, problems and exercises

Technical Papers | Laplace transform | Residue | Dynamic analysis | Pole | Partial fraction expansion | DECOMPOSITION | ENGINEERING, MECHANICAL | Mechanics | Usage | Laplace transformation | Research | Differential equations | Tests, problems and exercises

Journal Article

International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, 07/2017, Volume 48, Issue 5, pp. 802 - 808

We present a method for finding partial fraction decompositions of rational functions with linear or quadratic factors in the denominators by means of repeated polynomial divisions...

cover-up technique | polynomial division template | repeated polynomial divisions | Partial fraction decomposition | Validity | Mathematics Instruction | Equations (Mathematics) | Problem Solving | Mathematical Logic | Teaching Methods | Fractions

cover-up technique | polynomial division template | repeated polynomial divisions | Partial fraction decomposition | Validity | Mathematics Instruction | Equations (Mathematics) | Problem Solving | Mathematical Logic | Teaching Methods | Fractions

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 04/2019, Volume 69, Issue 2, pp. 327 - 338

.... By means of partial fraction decomposition, first the main theorems are proved and then some corollaries of them are...

Primary 11B39 | Secondary 05A30 | binomial coefficients | Fibonomial and Lucanomial coefficients | sums identites | partial fraction decomposition | Gaussian | Gaussian q-binomial coefficients | MATHEMATICS | GENERALIZED FIBONACCI | IDENTITIES | FIBONOMIAL SUMS

Primary 11B39 | Secondary 05A30 | binomial coefficients | Fibonomial and Lucanomial coefficients | sums identites | partial fraction decomposition | Gaussian | Gaussian q-binomial coefficients | MATHEMATICS | GENERALIZED FIBONACCI | IDENTITIES | FIBONOMIAL SUMS

Journal Article

Ars Combinatoria, ISSN 0381-7032, 2013, Volume 109, pp. 71 - 86

By means of partial fraction decomposition method, we evaluate a very general determinant of formal shifted factorial fractions, which covers numerous binomial...

MATHEMATICS | Partial fractions | The Cauchy double alternant | Binomial coefficients | NUMBERS | PATHS | CAUCHY DETERMINANT | ENUMERATION | PLANE PARTITIONS | Hankel determinant

MATHEMATICS | Partial fractions | The Cauchy double alternant | Binomial coefficients | NUMBERS | PATHS | CAUCHY DETERMINANT | ENUMERATION | PLANE PARTITIONS | Hankel determinant

Journal Article

MISKOLC MATHEMATICAL NOTES, ISSN 1787-2405, 2017, Volume 18, Issue 1, pp. 251 - 264

.... Our approach is straight-forward and simple. First we convert the sums in q-notation, then use partial fraction decomposition and telescoping to derive closed formul ae.

MATHEMATICS | partial fraction decomposition | reciprocal sums identities

MATHEMATICS | partial fraction decomposition | reciprocal sums identities

Journal Article

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