Polynomial series expansions for confluent and Gaussian hypergeometric functions

Mathematics of Computation

Volumn 74, Issue 252, 2005, Pages 1937-1952

  Luh, W ^a   Muller J ^a   Ponnusamy, S ^b   Vasundhra, P ^b  

^a UNIVERSITY OF TRIER   (Germany)

^b INDIAN INSTITUTE OF TECHNOLOGY MADRAS   (India)

Author keywords

Hadamard product; Hypergeometric series; Polynomial expansions

Indexed keywords

EID: 27144556589     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-05-01734-5     Document Type: Article

References (12)

1. M. ABRAMOWITZ AND I. STEGUN, Handbook of mathematical functions, Dover Publ., New York, 1968. MR0208798 (34:8607)
2. R. BALASUBRAMANIAN, S. PONNUSAMY, AND M. VUORINEN, On hypergeometric functions and function spaces, J. Comp. Appl. Math., 139(2002), 299-322. MR1876641 (2003a:33011)
3. A. ERDÉLYI, Higher transcendental functions, Vol. I of Bateman manuscript project, McGraw Hill, New York, 1953. MR0698779 (84h:33001a)
4. K.G. GROSSE-ERDMANN, On the Borel-Okada theorem and the Hadamard multiplication theorem, Complex Variables, 22(1993), 101-112. MR1277015 (95j:30002)
5. Y.L. LUKE, The special functions and their approximations, Vol.I, Academic Press, 1969. MR0241700 (39:3039)
6. Y.L. LUKE, The special functions and their approximations, Vol.II, Academic Press, 1969. MR0249668 (40:2909)
7. J. MÜLLER, The Hadamard multiplication theorem and applications in summability theory, Complex Variables, 18(1992), 155-166. MR1157924 (93g:30004)
8. J. MÜLLER, Convergence acceleration of Taylor sections by convolution, Constructive approximation, 15(1999), 523-536. MR1702803 (20001:41040)
9. CH. SCHWARZ, Computation of confluent hypergeometric functions and application to parabolic boundary control problems, Ph.D Thesis, University of Trier, 2001.
10. CH. SCHWARZ, Computation of confluent hypergeometric functions on compact intervals, In: Functions, Series, Operators (Budapest, 1999), 357-366, Janos Bolyai Math. Soc., Budapest, 2002. MR1981575 (2004g:33012)
11. N.M. TEMME, Special Functions: An introduction to the classical functions of mathematical physics, John Wiley, 1996. MR1376370 (97e:33002)
12. J.L. WALSH, Interpolation and approximation by rational functions in the complex domain, 5th ed., Amer. Math. Soc. Colloq. Publ., Providence, RI, 1969. MR0218588 (36:1672b)