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On some special polynomials
Author(s):
V.
V.
Karachik
Journal:
Proc. Amer. Math. Soc.
132
(2004),
1049-1058.
MSC (2000):
Primary 33D45;
Secondary 31B05, 35C05, 33D50
Posted:
November 25, 2003
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Abstract:
New special functions called  -functions are introduced. Connections of  -functions with the known Legendre, Chebyshev and Gegenbauer polynomials are given. For  -functions the Rodrigues formula is obtained.
References:
-
- [1]
- E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, Princeton, NJ, 1971. MR 46:4102
- [2]
- V. V. Karachik, Polynomial solutions to systems of partial differential equations with constant coefficients, Yokohama Mathematical Journal 47 (2) (2000), 121-142. MR 2001d:35031
- [3]
- V. V. Karachik, On one set of orthogonal harmonic polynomials, Proc. Amer. Math. Soc. 126 (12) (1998), 3513-3519. MR 99g:33034
- [4]
- A. Erdélyi, W. Magnus, F. Oberhettinger, and F. Tricomi, Higher Transcendental Functions, vol. 2, Based on notes left by Harry Bateman, McGraw-Hill, New York, 1953. MR 15:419i
- [5]
- E. D. Rainville, Special Functions, The Macmillan Company, New York, 1960. MR 21:6447
- [6]
- V. S. Vladimirov, Uravneniya matematicheskoj fiziki, Fiziko-Matematicheskaya Literatura, Moskva, 2000 (Russian).
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Additional Information:
V.
V.
Karachik
Affiliation:
148, Behterev St., Apt. 6, 700105, Tashkent, Uzbekistan
Address at time of publication:
Institute of Cybernetics, Uzbek Academy of Sciences, 34, F. Hodzhaev St., 700125, Tashkent, Uzbekistan
Email:
karachik@uwed.freenet.uz, karachik@tkt.uz
DOI:
10.1090/S0002-9939-03-07281-2
PII:
S 0002-9939(03)07281-2
Keywords:
Harmonic polynomials,
orthogonal polynomials
Received by editor(s):
November 5, 2002
Posted:
November 25, 2003
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2003,
American Mathematical Society
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