The Mittag-Leffler and Gamma Function

Name: The Mittag-Leffler and Gamma Function
Price: 227.95 AUD
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ISBN: 9780198993377

Piet Van Mieghem (Professor, Professor, Delft University of Technology)

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English

Oxford University Press
25 June 2026

Calculus; Functional analysis & transforms; Integral calculus & equations; Probability & statistics

Series: Oxford Mathematical Monographs

The Mittag-Leffler function is a basic function in fractional calculus and is an entire function in the complex plane. Entire functions are generalization of polynomials to infinite degree, do not have singularities in the complex plane, and possess a wealth of beautiful properties. Entire functions are defined by a Taylor series that converges for any finite complex number. In addition to the summation formulation and as a consequence of Weierstrass's factorization theorem, entire functions possess a product form in which all zeros appear. The study of properties of entire functions has led Mittag-Leffler, around 1900, to the study of his function. The Mittag-Leffler function is a primary example of an entire function, tunable in its order, and is represented by the simple eyeing Taylor series, in which another basic complex function, the Gamma function pops up. The Mittag-Leffler and Gamma Function mainly targets the mathematical properties of the Mittag-Leffler function in easy-to-understand language, not its applications to fractional analysis nor its numerical evaluation. Since the Gamma function plays a crucial role in the properties of the Mittag-Leffler function, a comprehensive treatment of the Mittag-Leffler function requires the knowledge of the Gamma function. The second part of the book attempts to present a complete study, enriched with historical references.

By: Piet Van Mieghem (Professor Professor Delft University of Technology)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
ISBN: 9780198993377
ISBN 10: 0198993374
Series: Oxford Mathematical Monographs
Pages: 352
Publication Date: 25 June 2026
Audience: College/higher education , Further / Higher Education
Format: Hardback
Publisher's Status: Forthcoming

Piet Van Mieghem is Professor at the Delft University of Technology with a chair in telecommunication networks that he broadened to Network Science. His main research interests lie in the analysis of complex networks such as infrastructural, biological, brain, social networks. He has published five books. He is an IEEE Fellow and received an Advanced ERC grant 2020 for Virus Spread in Networks. He was a visiting scientist at MIT (1992-1993) and a visiting professor at UCLA (2005), Cornell University (2009), Stanford University, and Princeton University (2022).