engleski

On multi-index Whittaker function and related integrals and inequalities

A new generalization of Whittaker function M_{; ; ; \lambda, \mu}; ; ; (z) is introduced and studied by means of the extended multi-index confluent hypergeometric function of the first kind \Phi_{; ; ; (\alpha_i, \beta_i)}; ; ; ^{; ; ; (\gamma_i), p}; ; ; introduced in [1]. The related Euler-type integral representation and the Laplace-Mellin and Hankel integral transforms are also presented. Functional two-sided bounding inequality is established for the multi-index Mittag-Leffler function, and in continuation functional lower bound is derived for the associated ML-extended Whittaker function.

Extended Whittaker function ; Extended confluent hypergeometric function ; Extended Beta function ; Multi-index Mittag-Leffler function ; Functional inequality bounds

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