A series of definite integrals involving upper incomplete Gamma functions

2025/02/15 by Mátyás Barczy, Barczy, Matyas, István Mező +1
Mathematics · Medicine · #33B20 #60E05 #Approximation Theory and Sequence Spaces #Calculus (dental) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Geology #Mathematical Inequalities and Applications #Mathematics #Medicine #Paleontology #Probability (math.PR) #Series (stratigraphy)

paper · pdf · doi:10.48550/arxiv.2502.10885

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Using probability theory we derive an expression for the sum of a series of definite integrals involving upper incomplete Gamma functions. In the proof, a normal variance mixture distribution with Beta mixing distributions plays a crucial role. We also give an interesting application of our result, namely, a new summation formula for some derivatives of the Bessel functions of the first kind and the Struve functions with respect to the order.

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