Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Special Issue on Asymptotics and Applications of Special Functions in Memory of Richard Paris

The Guest Editors for this special issue are

Mark Dunster (San Diego State University, USA)
David Kaminski (University of Lethbridge, Canada)
Dmitrii Karp (Holon Institute of Technology, Israel)
Gergő Nemes (Tokyo Metropolitan University, Japan)

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 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.

We welcome original research submissions on topics including, but not limited to:

  • asymptotics of integrals and special functions including orthogonal polynomials;
  • asymptotic solutions of differential and integral equations;
  • evaluation of sums and integrals;
  • transformations and identities for special functions and the functions of number theory and any further complex – or real – analytic properties of specific functions appearing when solving concrete problems in pure or applied mathematics.

There is no limit to the length of an article. Deadline for paper submission is March 31, 2024.

How to Submit an Article to the Issue.

All articles will go through the standard peer reviewing procedure of SIGMA.

Papers in this Issue:

Resurgence in the Transition Region: The Incomplete Gamma Function
Gergő Nemes
SIGMA 20 (2024), 026, 14 pages   [ abs   pdf ]
Lerch $\Phi$ Asymptotics
Adri B. Olde Daalhuis
SIGMA 20 (2024), 023,   9 pages   [ abs   pdf ]
On the Hill Discriminant of Lamé's Differential Equation
Hans Volkmer
SIGMA 20 (2024), 021,   9 pages   [ abs   pdf ]
A Note on the Equidistribution of 3-Colour Partitions
Joshua Males
SIGMA 20 (2024), 001,   8 pages   [ abs   pdf ]
Sun's Series via Cyclotomic Multiple Zeta Values
Yajun Zhou
SIGMA 19 (2023), 074, 20 pages   [ abs   pdf ]

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