Numeric-analytical construction of Mathieu functions

Yu. A. Ryabov

Mathematica Bohemica (1999)

  • Volume: 124, Issue: 1, page 15-28
  • ISSN: 0862-7959

Abstract

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In this paper we present an iterative algorithm for the construction of Mathieu functions of any order in the form of Fourier series (practically, polynomials), and also the corresponding Quick-BASIC program for realization of this algorithm with numerical values of the parameter.

How to cite

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Ryabov, Yu. A.. "Numeric-analytical construction of Mathieu functions." Mathematica Bohemica 124.1 (1999): 15-28. <http://eudml.org/doc/248447>.

@article{Ryabov1999,
abstract = {In this paper we present an iterative algorithm for the construction of Mathieu functions of any order $N$ in the form of Fourier series (practically, polynomials), and also the corresponding Quick-BASIC program for realization of this algorithm with numerical values of the parameter.},
author = {Ryabov, Yu. A.},
journal = {Mathematica Bohemica},
keywords = {Mathieu functions; iterative algorithm; Quick-BASIC program; Fourier series; Mathieu functions; iterative algorithm; Quick-BASIC program; Fourier series},
language = {eng},
number = {1},
pages = {15-28},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Numeric-analytical construction of Mathieu functions},
url = {http://eudml.org/doc/248447},
volume = {124},
year = {1999},
}

TY - JOUR
AU - Ryabov, Yu. A.
TI - Numeric-analytical construction of Mathieu functions
JO - Mathematica Bohemica
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 124
IS - 1
SP - 15
EP - 28
AB - In this paper we present an iterative algorithm for the construction of Mathieu functions of any order $N$ in the form of Fourier series (practically, polynomials), and also the corresponding Quick-BASIC program for realization of this algorithm with numerical values of the parameter.
LA - eng
KW - Mathieu functions; iterative algorithm; Quick-BASIC program; Fourier series; Mathieu functions; iterative algorithm; Quick-BASIC program; Fourier series
UR - http://eudml.org/doc/248447
ER -

References

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  1. Ch. Hayashi, Nonlinear Oscillations in Physical Systems, McGraw-Hill, New York, 1964. (1964) Zbl0192.50605MR0170071
  2. Yu. A. Ryabov, The estimations of convergence radius for series in power of parameter and algorithms for construction of Mathieu functions, Differencialnye uravnenija 15 (1979), no. 11, 1993-2003. (In Russian.) (1979) MR0554259
  3. B. A. Grebenikov, Yu. A. Ryabov, Constructive methods in the analysis of nonlinear systems, Mir Publishers, Moscow, 1983, translated from Russian. (1983) Zbl0536.65058MR0733787

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