• the hermite pade approximation...

Result: the hermite pade approximations of generalized hypergeometric series in two variables: Hermite-Padé approximations of generalized hypergeometric series in two variables

Title:
the hermite pade approximations of generalized hypergeometric series in two variables: Hermite-Padé approximations of generalized hypergeometric series in two variables
Authors:
V. N. Sorokin
Source:
Siberian Mathematical Journal. 43(4):719-730
Publisher Information:
Russian Academy of Sciences - RAS (Rossiĭskaya Akademiya Nauk - RAN), Siberian Branch (Sibirskoe Otdelenie), Sobolev Insitute of Mathematics (Institut Matematiki Im. S. L. Soboleva), Novosibirsk, 2002.
Publication Year:
2002
Subject Terms:
Irrationality, linear independence over a field, Hermite-Padé approximation, Numerical approximation and evaluation of special functions, orthogonal polynomial, Appell polynomials, integral representation, Padé approximation
Document Type:
Academic journal Article
File Description:
application/xml
ISSN:
0037-4466
DOI:
10.1023/a:1016336605594
Access URL:
https://zbmath.org/1882385
https://link.springer.com/content/pdf/10.1023/A:1016336605594.pdf
Accession Number:
edsair.dedup.wf.002..00540013ef2c81e8dba48a1e8403b0fc
Database:
OpenAIRE

Further Information

Summary: We give examples of well-posed problems of joint Hermite-Padé approximations of series in two variables. We find Rodrigues formulas and integral representations for solutions. We also study the limit distribution of zeros of the corresponding polynomials. The constructions are based, on the one hand, on the classical Appell polynomials orthogonal in a triangle and, on the other hand, on various ways of proving Apéry's theorem about irrationality of the number \(\zeta (3)\).