Results 1 to 10 of about 12,909 (197)
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 note on Appell sequences, Mellin transforms and Fourier series [PDF]
Journal of Mathematical Analysis and Applications, 2019 A large class of Appell polynomial sequences {p n (x)} n=0 8 are special values at the negative integers of an entire function F(s, x), given by the Mellin transform of the generating function for the sequence. For the Bernoulli and Apostol-Bernoulli polynomials, these are basically the Hurwitz zeta function and the Lerch transcendent.
Luis M. Navas +2 more
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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 Abstract 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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An Appell series over finite fields
Finite Fields and Their Applications, 2017 In this paper we present a finite field analogue for one of the Appell series. We shall derive its transformations, reduction formulas as well as generating functions.
Bing He, Long Li, Ruiming Zhang
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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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Multiple Hypergeometric Series: Appell Series and Beyond [PDF]
, 2013 17 ...
Michael J. Schlosser
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, 2021 Archinard studied the curve $C$ over $\mathbb{C}$ associated to an Appell-Lauricella hypergeometric series and differential forms on its desingularization. In this paper, firstly as a generalization of Archinard's results, we describe a partial desingularization of $C$ over a field $K$ under a mild condition on its characteristic and the space of ...
Ryo Ohashi, Shushi Harashita
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A finite field analogue for Appell series F_3
, 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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A finite sum representation of the Appell series F1(a,b,b′;c;x,y)
Journal of Computational and Applied Mathematics, 1999 AbstractWe use Picard's integral representation of the Appell series F1(a,b,b′;c;x,y) for Re(a)>0,Re(c−a)>0 to obtain a finite sum algebraic representation of F1 in the case when a,b,b′ and c are positive integers with c>a. The series converges for |x|
Annie Cuyt +3 more
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