×
Lin, Shy-Der; Liu, Shuoh-Jung; Srivastava, H. M.

Some families of hypergeometric polynomials and associated multiple integral representations. (English) Zbl 1258.33007

Integral Transforms Spec. Funct. 22, No. 6, 403-414 (2011).
Summary: The main object of this paper is to investigate several general families of hypergeometric polynomials and their associated multiple integral representations. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials.

Cited in 5 Documents

MSC:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
33C65 Appell, Horn and Lauricella functions
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis

Keywords:

hypergeometric polynomials; integral representations; gamma function; Eulerian beta integral; generalized Rice polynomials; generating functions; Srivastava polynomials; Lagrange polynomials; Lagrange-Hermite polynomials; Pochhammer symbol; Hermite-Kampé de Fériet polynomials
Cite Review PDF
Full Text: DOI

References:

[1] DOI: 10.1080/10652460600568162 · Zbl 1099.26010 · doi:10.1080/10652460600568162
[2] DOI: 10.1080/10652460108819340 · Zbl 1057.33003 · doi:10.1080/10652460108819340
[3] DOI: 10.1017/S1446181100012815 · Zbl 1148.33002 · doi:10.1017/S1446181100012815
[4] Erdélyi A., Higher Transcendental Functions (1953) · Zbl 0051.30303
[5] Erdélyi A., Higher Transcendental Functions (1955) · Zbl 0064.06302
[6] DOI: 10.1080/10652460500444928 · Zbl 1098.33016 · doi:10.1080/10652460500444928
[7] DOI: 10.1016/j.amc.2006.01.090 · Zbl 1103.41024 · doi:10.1016/j.amc.2006.01.090
[8] DOI: 10.1016/S0895-7177(01)00053-X · Zbl 0991.33010 · doi:10.1016/S0895-7177(01)00053-X
[9] Khandekar P. R., Proc. Nat. Acad. Sci. India Sect. A 34 pp 157– (1964)
[10] DOI: 10.1016/S0895-7177(02)00113-9 · Zbl 1129.90314 · doi:10.1016/S0895-7177(02)00113-9
[11] DOI: 10.1016/j.jmaa.2004.01.024 · Zbl 1048.33012 · doi:10.1016/j.jmaa.2004.01.024
[12] DOI: 10.1080/10652460500105370 · Zbl 1085.33006 · doi:10.1080/10652460500105370
[13] DOI: 10.1080/10652460802568291 · Zbl 1187.33005 · doi:10.1080/10652460802568291
[14] Magnus W., Formulas and Theorems for the Special Functions of Mathematical Physics (Die Grundlehren der Mathematischen Wissenschften in Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete) (1966) · Zbl 0143.08502 · doi:10.1007/978-3-662-11761-3
[15] Manocha H. L., Collect. Math 20 pp 117– (1969)
[16] DOI: 10.1016/j.mcm.2009.05.030 · Zbl 1185.33014 · doi:10.1016/j.mcm.2009.05.030
[17] Srivastava H. M., Indian J. Math 14 pp 1– (1972)
[18] Srivastava H. M., Collect. Math 24 pp 117– (1973)
[19] Srivastava H. M., Rev. Acad. Canaria Cienc 14 pp 25– (2002)
[20] Srivastava H. M., Acad. Roy. Belg. Bull. Cl. Sci 60 pp 919– (1974)
[21] Srivastava H. M., A Treatise on Generating Functions (1984) · Zbl 0535.33001
[22] DOI: 10.1112/jlms/s2-12.4.419 · Zbl 0304.33015 · doi:10.1112/jlms/s2-12.4.419
[23] DOI: 10.1080/10652469.2010.481439 · Zbl 1223.33019 · doi:10.1080/10652469.2010.481439
[24] Whittaker E. T., A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions, 4. ed. (1927) · JFM 53.0180.04
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.