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Article

Lin, Shy-Der ; Liu, Shuoh-Jung ; Lu, Han-Chun ; Srivastava, Hari Mohan
Linearization relations for the generalized Bedient polynomials of the first and second kinds via their integral representations. (English). Czechoslovak Mathematical Journal, vol. 63 (2013), issue 4, pp. 969-987
MSC: 33C45, 33C65, 42C05 | MR 3165508 | Zbl 06373955 | DOI: 10.1007/s10587-013-0065-6
Keywords:
hypergeometric function; hypergeometric polynomial; Srivastava polynomial; Bedient polynomial; generalized Bedient polynomial of the first and second kinds; multiple integral representation; Gamma function; Eulerian beta integral linearization relationship; Pochhammer symbol; shifted factorial
Summary:
The main object of this paper is to investigate several general families of hypergeometric polynomials and their associated multiple integral representations. By suitably specializing our main results, the corresponding integral representations are deduced for such familiar classes of hypergeometric polynomials as (for example) the generalized Bedient polynomials of the first and second kinds. 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.
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