Reprint

Special Functions with Applications to Mathematical Physics

Edited by
March 2023
438 pages
  • ISBN978-3-0365-6990-1 (Hardback)
  • ISBN978-3-0365-6991-8 (PDF)

This book is a reprint of the Special Issue Special Functions with Applications to Mathematical Physics that was published in

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Summary

This MDPI booklet lists the articles published in three Special Issues of the journal Mathematics devoted to special functions with applications in mathematical physics in the years 2020–2021.The call for papers considered theories and applications of high transcendental functions, including topics found mainly in the list of keywords:- Mittag-Leffler and related functions, and their applications in mathematical physics;- Wright and related functions and their applications in mathematical physics;- exponential integrals and their extensions with applications in mathematical physics;- generalized hypergeometric functions and their extensions with applicationsHowever, the Special Issues were not limited to the above list, for example, when the content of a paper was clearly related to some high transcendental functions and their applications.Special attention was reserved for distinct functions exhibiting some relevance in the framework of the theories and applications of the fractional calculus and in their visualization through illuminating plots.Both research and survey articles were included in this booklet, according to the content list.

Format
  • Hardback
License
© by the authors
Keywords
asymptotic expansions; exponential integral; Mittag-Leffler function; sine and cosine integrals; Mellin convolutions; Krätzel integrals; reaction-rate probability integral; continuous mixtures; Bayesian structures; fractional integrals; statistical distribution of products and ratios; multivariate and matrix-variate cases; real and complex domains; derivatives with respect to parameters; Mittag-Leffler functions; Laplace transform approach; infinite power series; integral representations; convolution integrals; quotients of digamma and gamma functions; fractional calculus; Wright functions; Green’s functions; diffusion-wave equation; Laplace transform; four-parameters Wright function of the second kind; one-dimensional time-fractional diffusion-wave equation; scale-invariant solutions; multi-dimensional space-time-fractional diffusion equation; subordination formula; left- and right-hand sided Erdélyi-Kober fractional derivatives; asymptotic series; asymptotic form; Borel summation; complete asymptotic expansion; divergent series; domain of convergence; gamma function; Mellin–Barnes regularization; regularization; remainder; Stokes discontinuity; Stokes line/sector; Stokes phenomenon; Stirling’s formula; generalized hypergeometric function; hypergeometric transformations; transformation groups; symmetric group; Laguerre-type derivative; Laguerre-type exponentials; Laguerre-type special functions; multivariable and multi-index Laguerre polynomials; population dynamics models; Laguerre-type linear dynamical systems; generalized integral transform; generalized convolution product; bounded linear operator; Gaussian process; Cameron–Storvick theorem; translation theorem; special functions; generalized hypergeometric functions; fractional calculus operators; integral transforms; non-central χ2 distribution; second mean-value theorem for definite integrals; modified Bessel function of the first kind; Marcum Q–function; lower incomplete gamma function; fractional calculus; Caputo derivative; Mittag–Leffler functions; Wright function; Mainardi function; Laplace transform; Fourier transform; nonperfect thermal contact; nonlocal elasticity; fractional nonlocal elasticity; complete monotonicity; convex ordering; double Gamma function; fractional extreme distribution; Kilbas-Saigo function; Le Roy function; Mittag–Leffler function; stable subordinator; multistage differential transformation method; Duffing equation; nonlinear damping oscillations; bateman functions; havelock functions; integral-bateman functions; confluent hypergeometric functions; Le Roy functions and series in them; inequalities; asymptotic formula; convergence of power and functional series in complex plane; Cauchy–Hadamard, Abel, Tauber and Littlewood type theorems; wright function; asymptotic expansions; Stokes phenomenon; fractional integrals and derivatives; Grünwald-Letnikov approach; Sonine kernel; Nekrasov fractional derivative; Sonine kernel; Sonine condition; general fractional derivative; general fractional integral; convolution series; fundamental theorems of fractional calculus; fractional differential equations; Hilbert space; convolution product; first variation; integration by parts formula; translation theorem; railway transport; roadbed; geodynamic processes; seismoelectric method; stress–strain process; transfer functions; frequency characteristics; phasometric method; laboratory modeling; integral Mittag-Leffler functions; integral Whittaker functions; integral Wright functions; Laplace transforms; n/a