Novel Identities for the H-Function: Applications to Hypergeometric Series Summation and Computational Efficiency in Special Function Analysis
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The H-function is a generalizable mathematical construction with applications in many areas, including special function analysis and hypergeometric series summation; this work presents new identities for it. Improving computing efficiency in mathematics and practical sciences and simplifying the summing of hypergeometric series are two goals of the study that seek to derive and validate these identities. The suggested identities are shown to be effective in decreasing computing complexity and increasing accuracy through analytical proofs and comparisons to current approaches. We show how these identities might be used in symbolic computation and numerical algorithms by examining certain cases. In addition, the research assesses how well these identities operate in special function analysis, which sheds light on how to incorporate them into computational frameworks. The results open the door to future developments in efficient handling of complicated special functions and make a substantial contribution to computer mathematics and mathematical analysis. Both theoretical and practical investigations in a wide range of scientific fields can benefit from this study.
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