# Special Functions with Applications to Mathematical Physics

- ISBN978-3-0365-6990-1 (Hardback)
- ISBN978-3-0365-6991-8 (PDF)

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

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.

- Hardback

*χ*2 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