Some finite summation formulas involving multivariable hypergeometric polynomials. (English) Zbl 1040.33008
The multinomial theorem is applied in connection with a representation of a multinomial polynomial in order to obtain a general finite summation formula. Specific cases include a finite summation formula for generalized Lauricella polynomials. A second general result is obtained from a multiple series identity. Further results are produced from a multiple sum formula for which the multinomial theorem is a limiting case.
Various special cases involve finite sums of Lauricella functions of r variables, as well as other special functions.
Various special cases involve finite sums of Lauricella functions of r variables, as well as other special functions.
Reviewer: Robert G. Buschman (Langlois)
MSC:
33C65 | Appell, Horn and Lauricella functions |
33C50 | Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable |
References:
[1] | Appell P., Fonctions Hypergéométriques et Hypersphériques; Polynômes d’Hermite (1926) |
[2] | Carlitz L., Mat. Vesnik 13 pp 41– (1976) |
[3] | Carlson B. C., Special Functions of Applied Mathematics (1977) · Zbl 0394.33001 |
[4] | Djordjevic, L. N. 1977. ”On a new class of cubature formulas”. University of Ni? Ni? (Serbian). Doctoral thesis, |
[5] | Djordjevic L. N., Novi Sad J. Math. 30 pp 31– (2000) |
[6] | DOI: 10.1137/0522017 · Zbl 0727.33002 · doi:10.1137/0522017 |
[7] | DOI: 10.1139/p85-239 · Zbl 1043.81570 · doi:10.1139/p85-239 |
[8] | Panda R., Jñanabha Sect. A 4 pp 165– (1974) |
[9] | Srivastava H.M, Multiple Gaussian Hypergeometric Series (1985) |
[10] | Szego G., Orthogonal Polynomials, 23, 4. ed. (1975) |
[11] | Toscano L., Matematiche (Catania) 27 pp 219– (1972) |
[12] | DOI: 10.1063/1.527898 · Zbl 0647.42014 · doi:10.1063/1.527898 |
[13] | DOI: 10.1063/1.528430 · Zbl 0661.33010 · doi:10.1063/1.528430 |
[14] | DOI: 10.1063/1.528237 · Zbl 0687.33014 · doi:10.1063/1.528237 |
[15] | DOI: 10.1063/1.528507 · Zbl 0696.33010 · doi:10.1063/1.528507 |
[16] | DOI: 10.1063/1.528697 · Zbl 0707.33007 · doi:10.1063/1.528697 |
[17] | DOI: 10.1063/1.529228 · Zbl 0746.33007 · doi:10.1063/1.529228 |
[18] | DOI: 10.1063/1.529158 · Zbl 0742.33007 · doi:10.1063/1.529158 |
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.