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Going Next after “A Guide to Special Functions in Fractional Calculus”: A Discussion Survey
MathematicsIn the survey Kiryakova: “A Guide to Special Functions in Fractional Calculus” (published in this same journal in 2021) we proposed an overview of this huge class of special functions, including the Fox H-functions, the Fox–Wright generalized ...
Virginia Kiryakova +1 more
doaj +2 more sources
General Overview of Multivariable Special Functions [PDF]
, 2020 This chapter gives an introduction to the book. It surveys multivariable hypergeometric series and integrals, with comparison of the classical, basic and elliptic case, and multivariable (bi)orthogonal polynomials and functions, where root system ...
J. V. Stokman +3 more
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New Results of the Fifth-Kind Orthogonal Chebyshev Polynomials
, 2021 The principal objective of this article is to develop new formulas of the so-called Chebyshev polynomials of the fifth-kind. Some fundamental properties and relations concerned with these polynomials are proposed.
Seraj Omar Alkhamisi +1 more
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Uniform asymptotics of some q-orthogonal polynomials [PDF]
, 2010 Uniform asymptotic formulas are obtained for the Stieltjes–Wigert polynomial, the q−1-Hermite polynomial and the q-Laguerre polynomial as the degree of the polynomial tends to infinity.
Wang, X.S., Wong, R.
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On Certain Wronskians of Multiple Orthogonal Polynomials [PDF]
, 2014 . We consider determinants of Wronskian type whose entries are multiple ortho-gonal polynomials associated with a path connecting two multi-indices. By assuming that the weight functions form an algebraic Chebyshev (AT) system, we show that the poly ...
Zhang, L. +3 more
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Continued Fractions and Orthogonal Polynomials on the Unit Circle
, 2005 Khrushchev, Sergey/0000-0002-8854-5317This survey is written to stress the role of continued fractions in the theory of orthogonal polynomials on the line and on the circle.
Khrushchev, S, Khrushchev, Sergey
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پژوهشهای ریاضی, 2020 Introduction Despite wide applications of constant order fractional derivatives, some systems require the use of derivatives whose order changes with respect to other parameters.
Farideh Salehi +2 more
doaj
Advanced Functional Materials, EarlyView.Printed negative‐dielectric‐anisotropy liquid‐crystal droplets enable multidimensional full‐vectorial optical‐field sensing across polarization, phase, and wavelength, while also generating tunable skyrmionic‐like complex optical fields. ABSTRACT Adaptive manipulation of vectorial optical fields is important for optical metrology, imaging, and ...
Jinge Guo +14 more
wiley +1 more source
Hahn's generalized problem and corresponding Appell sequences [PDF]
, 2008 This thesis is devoted to some aspects of the theory of orthogonal polynomials, paying a special attention to the classical ones (Hermite, Laguerre, Bessel and Jacobi).
Loureiro, Ana F.
core
Some bilateral generating functions for a certain class of special functions. I [PDF]
, 1980 The object of this paper is to present a systematic introduction to and several interesting applications of a general method of obtaining bilinear, bilateral or mixed multilateral generating functions for a fairly wide variety of special functions in one,
Srivastava, H.M.
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