CERTAIN RECURRENCE RELATIONS OF GENERALIZED  $M$-SERIES AND ITS APPLICATION TO STATISTICAL  DISTRIBUTION

Dheerandra Shanker Sachan; Dinesh Kumar; D.L. Suthar; K.S. Nisar

doi:10.5269/bspm.76299

Dheerandra Shanker Sachan St. Mary's PG College Vidisha(MP) India https://orcid.org/0000-0002-9400-3223
Dinesh Kumar Department of Applied Sciences, College of Agriculture-Jodhpur, Agriculture University Jodhpur, Jodhpur–342304 (Raj.), INDIA https://orcid.org/0000-0001-5415-1777
D.L. Suthar Department of Mathematics, Wollo University, P.O. Box 1145, Dessie, Ethiopia. https://orcid.org/0000-0001-9978-2177
K.S. Nisar Department of Mathematics, College of Science and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj, 11942, Saudi Arabia. https://orcid.org/0000-0001-5769-4320

Résumé

This paper addresses the prominent field of research concerning recurrence
relations for special functions. Recognizing the significance of this area, we present
a novel contribution by introducing new recurrence relations specifically designed for
generalized M-Series. Through our analysis, we uncover intriguing connections between
(p+q+1) and (p+q+2) parametric M-Series, which emerge as a direct consequence of
these newly established recurrence relations. Furthermore, we leverage these relations
to derive additional recurrence relations for both the Fox-Wright function and the
generalized hypergeometric function, serving as noteworthy corollaries to our main
findings. In addition, we explore the application of M-series in the establishment of
distribution functions, ultimately enabling us to determine the Laplace transform of
the density function. By delving into these interrelated topics, our research expands the
understanding and knowledge base in this field, paving the way for further exploration
and advancements.

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