The Application of Real Convolution for Analytically Evaluating Fermi-Dirac-Type and Bose-Einstein-Type Integrals | Zendy

Jerry P. Selvaggi | Zendy; Jerry A. Selvaggi | Zendy

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The Application of Real Convolution for Analytically Evaluating Fermi-Dirac-Type and Bose-Einstein-Type Integrals

Author(s) -

Jerry P. Selvaggi,

Jerry A. Selvaggi

Publication year - 2018

Publication title -

journal of complex analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.167

H-Index - 7

eISSN - 2314-4963

pISSN - 2314-4971

DOI - 10.1155/2018/5941485

Subject(s) - laplace transform , convolution (computer science) , fermi–dirac statistics , type (biology) , slater integrals , transformation (genetics) , mathematical analysis , convolution theorem , fermi gamma ray space telescope , mathematics , multiple integral , numerical integration , physics , quantum mechanics , computer science , fourier transform , electron , ecology , biochemistry , chemistry , fourier analysis , machine learning , artificial neural network , gene , fractional fourier transform , biology

The Fermi-Dirac-type or Bose-Einstein-type integrals can be transformed into two convergent real-convolution integrals. The transformation simplifies the integration process and may ultimately produce a complete analytical solution without recourse to any mathematical approximations. The real-convolution integrals can either be directly integrated or be transformed into the Laplace Transform inversion integral in which case the full power of contour integration becomes available. Which method is employed is dependent upon the complexity of the real-convolution integral. A number of examples are introduced which will illustrate the efficacy of the analytical approach.

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