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Special Issue on Asymptotics and Applications of Special Functions in Memory of Richard Paris
The Guest Editors for this special issue are
This special issue is in honor of the memory of Professor Richard Bruce Paris (1946–2022) who passed away on July 8, 2022, shortly after being diagnosed with a serious illness. Richard Paris was Reader in Mathematics at the University of Abertay Dundee, UK and had an honorary appointment at the University of St. Andrews, UK. Richard was an expert in asymptotics and special functions who published prolifically with over 150 papers listed on MathSciNet. Richard's contributions to special functions and asymptotics are numerous and diverse. A good sense of the range of his research is captured in the three monographs he left with us. In the first, Asymptotics of High Order Differential Equations, written in collaboration with Alastair Wood, he showcased the use of integrals of hypergeometric type in the solution of several classes of differential equations. This was further elaborated in a second monograph, Asymptotics and Mellin–Barnes Integrals, written with David Kaminski, in which they explored the use of Mellin–Barnes integrals in asymptotic analysis. His final monograph, Hadamard Expansions and Hyperasymptotic Evaluation – a solo effort – extended his integral-theoretic analyses to high precision asymptotics, with a particular emphasis on errors committed by such approximations. Among his other achievements are: generalizations of Euler, Pfaff, Kummer and quadratic transformations to generalized hypergeometric functions with integral parameter differences and numerous summation and transformations formulas resulting from them; the theory of extended hypergeometric functions obtained by introducing additional factors into standard integral representations; evaluation of integrals and multiple hypergeometric series arising from field theories; properties of Wright's function and generalizations; explicit evaluations of various sums and integrals. The volume consists of 9 papers for a total of 118 pages. We are grateful to all the authors who contributed to this volume and to the referees for providing constructive reviews.
The Guest Editors
Papers in this Issue:
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