A family of summation formulas on the Fox–Wright function

Wei, Chuanan; Gong, Daozhi; Hu, Hao

doi:10.1016/j.jmaa.2012.03.008

Cited by 5 publications

(2 citation statements)

References 30 publications

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“…See also [39, section 6] for an application in information theory. It has been a recent surge of interest in the Fox-Wright function as witnessed by the articles [16,36,37,43,44,45,48,52,54]. The papers [16,54] establish summation formulas for the Fox-Wright function using combinatorial inversion formulas.…”

Section: Introductionmentioning

confidence: 99%

“…It has been a recent surge of interest in the Fox-Wright function as witnessed by the articles [16,36,37,43,44,45,48,52,54]. The papers [16,54] establish summation formulas for the Fox-Wright function using combinatorial inversion formulas. In [52] the author used a somewhat opposite approach by first developing contiguous relations for the Fox-Wright function and then employing them to prove Hagen-Rothe convolutions from combinatorics.…”

Section: Introductionmentioning

confidence: 99%

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The Fox-Wright function near the singularity and the branch cut

Karp

Prilepkina

2020

Journal of Mathematical Analysis and Applications

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The Fox-Wright function is a further extension of the generalized hypergeometric function obtained by introducing arbitrary positive scaling factors into the arguments of the gamma functions in the summand. Its importance comes mostly from its role in fractional calculus although other interesting applications also exist. If the sums of the scaling factors in the top and bottom parameters are equal, the series defining the Fox-Wright function has a finite non-zero radius of convergence. It was demonstrated by Braaksma in 1964 that the Fox-Wright function can then be extended to a holomorphic function in the complex plane cut along a ray from the positive point on the boundary of the disk of convergence to the point at infinity. In this paper we study the behavior of the Fox-Wright function in the neighborhood of this positive singular point. Under certain restrictions we give a convergent expansion with recursively computed coefficients completely characterizing this behavior. We further compute the jump and the average value of the Fox-Wright function on the banks of the branch cut.

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