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A Simple Algorithm for the Evaluation of a Class of Generalized Hypergeometric Series
Author(s) -
Srivastava H. M.
Publication year - 1992
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm199286179
Subject(s) - generalized hypergeometric function , basic hypergeometric series , series (stratigraphy) , simple (philosophy) , mathematics , hypergeometric identity , hypergeometric function of a matrix argument , bilateral hypergeometric series , class (philosophy) , hypergeometric function , confluent hypergeometric function , operator (biology) , algebra over a field , calculus (dental) , connection (principal bundle) , riemann hypothesis , pure mathematics , computer science , geometry , philosophy , dentistry , artificial intelligence , paleontology , epistemology , medicine , repressor , chemistry , biology , biochemistry , transcription factor , gene
Making use of a remarkably simple algorithm, the author evaluates the sum of a certain class of generalized hypergeometric series of unit argument. It is also shown how closely this main summation formula is related to other (known or new) evaluations of lower‐order hypergeometric series. Finally, the author highlights the connection of his main result with a well‐known sum which happens to have attracted considerable attention in many recent works demonstrating the usefulness of the Riemann‐Liouville operator of fractional calculus.