A NEW LOOK AT q-HYPERGEOMETRIC FUNCTIONS

Yıl 2014, Cilt: 4 Sayı: 1, 16 - 19, 01.06.2014

M. Darus

Öz

For complex parameters ai, bj , q i = 1, ..., r, j = 1, ..., s, bj ∈ C\{0, −1, −2, ...}, |q| < 1 , define the q-hypergeometric function rΦs a1, ..., ar; b1, ..., bs; q, z by rΦs ai; bj ; q, z = ∑∞ n=0 a1, q n... ar, q n q, q n b1, q n... bs, q n z n r = s + 1; r, s ∈ N0 = N ∪ {0}; z ∈ U where N denote the set of positive integers and a, q n is the q-shifted factorial defined by a, q n = { 1, n = 0; 1 − a 1 − aq 1 − aq2 ... 1 − aqn−1 , n ∈ N. Recently, the authors [7] defined the linear operator M ai, bj ; q f. Using the operator M ai, bj ; q f z f, Aldweby and Darus [13] gave a new integral operator. In this work we highlight a result related to the new integral operator.

Anahtar Kelimeler

q-hypergeometric functions, Integral operators

Kaynakça

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