Finite-part integration of the generalized Stieltjes transform and its dominant asymptotic behavior for small values of the parameter. II. Non-integer orders

DOI10.1063/1.5038900zbMath1406.44004arXiv1805.01734OpenAlexW4242150869MaRDI QIDQ4621269

Christian D. Tica, Eric A. Galapon

Publication date: 11 February 2019

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.01734

zbMATH Keywords

asymptotic behaviorasymptotic expansionGreen-Kubo formulageneralized Stieltjes transformPeclet numberfinite-part integration

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Best approximation, Chebyshev systems (41A50)

Related Items (2)

Regularized limit, analytic continuation and finite-part integration ⋮ Finite-part integration in the presence of competing singularities: Transformation equations for the hypergeometric functions arising from finite-part integration

Uses Software

• DLMF

Cites Work

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• Hypergeometric functions as generalized Stieltjes transforms
• Definitions, properties and applications of finite-part integrals
• A theorem on the generalized Stieltjes transform and its applications
• On a generalized Stieltjes transform
• The Cauchy principal value and the Hadamard finite part integral as values of absolutely convergent integrals
• Finite-part integration of the generalized Stieltjes transform and its dominant asymptotic behavior for small values of the parameter. I. Integer orders
• The problem of missing terms in term by term integration involving divergent integrals
• The Stieltjes Transform

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