Results 1 to 10 of about 13,281 (168)
Multiple Hypergeometric Series: Appell Series and Beyond [PDF]
, 2013 17 ...
Michael J. Schlosser
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Some properties of generalized hypergeometric Appell polynomials [PDF]
Karpatsʹkì Matematičnì Publìkacìï, 2020 Let $x^{(n)}$ denotes the Pochhammer symbol (rising factorial) defined by the formulas $x^{(0)}=1$ and $x^{(n)}=x(x+1)(x+2)\cdots (x+n-1)$ for $n\geq 1$.
L. Bedratyuk, N. Luno
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REMARKS FOR BASIC APPELL SERIES [PDF]
Honam Mathematical Journal, 2009 Let k be an imaginary quadratic fleld, H the complex upper half plane, and let ? 2 k\H, q = exp(…i?). And let n;t be positive integers with 1 • tni1. Then q n 12 i t 2 + t2 2n Q 1 m=1 (1iq nmit)(1iqnmi (nit)) is an algebraic number (10). As a generalization of this result, we flnd several inflnite series and products giving algebraic numbers using ...
Gyeong-Sig Seo, Joong-Soo Park
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A finite field analogue for Appell series F_3 [PDF]
, 2017 In this paper we introduce a finite field analogue for the Appell series F_3 and give some reduction formulae and certain generating functions for this function over finite fields.
Bing He
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Mock theta functions and Appell–Lerch sums [PDF]
Journal of Inequalities and Applications, 2018 Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function g2(x,q) $g_{2}{(x,q)}$.
Bin Chen
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On the mock-theta behavior of Appell–Lerch series
Comptes Rendus. Mathématique, 2015 The goal of this paper is to find one natural way to write the first order Appell–Lerch series in terms of two functions whose asymptotic behavior becomes simple. It is shown that such writing exists, using only theta-like functions and functions having a Gevrey asymptotic expansion.
Changgui Zhang
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A finite field analogue of the Appell series $F_4$ [PDF]
, 2018 We define a function $F_4^{\ast}$ as a finite field analogue of the classical Appell series $F_4$ using Gauss sums. We establish identities for $F_4^{\ast}$ analogous to those satisfied by the classical Appell series $F_4$.
Mohit Tripathi, Rupam Barman
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Another finite field analogue for Appell series F_{1} [PDF]
, 2017 In this paper we introduce another finite field analogue for Appell series F_{1} and obtain certain reduction formulae and a generating function for this analogue.
Bing He
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European Physical Journal C: Particles and Fields, 2020 Based on the method developed in Phan and Riemann (Phys Lett B 791:257, 2019), detailed analytic results for scalar one-loop two-, three-, four-point integrals in general d-dimension are presented in this paper.
Khiem Hong Phan
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Bibasic $q$-Appell series connected with Ramanujan's continued fractions
Tamkang Journal of Mathematics, 2007 In this paper we give some summation formulae for bibasic $ q $-Appell function $ \overline{\varphi}^{(1)} $ and express Appell function $ \overline{\varphi}^{(1)} $ in terms of classical continued fractions of Ramanujan. We also express the $ q $-Appell function $ \varphi^{(1)} $ on one base as a continued fraction. The bibasic approach for the Appell
Bhaskar Srivastava
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