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:
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