Results 11 to 20 of about 44 (30)

New Relations Involving an Extended Multiparameter Hurwitz‐Lerch Zeta Function with Applications

International Journal of Analysis, Volume 2014, Issue 1, 2014., 2014
We derive several new expansion formulas involving an extended multiparameter Hurwitz‐Lerch zeta function introduced and studied recently by Srivastava et al. (2011). These expansions are obtained by using some fractional calculus methods such as the generalized Leibniz rules, the Taylor‐like expansions in terms of different functions, and the ...
H. M. Srivastava, Sébastien Gaboury, Richard Tremblay, Shamsul Qamar   +3 more
wiley   +1 more source

Appell-Lerch Sums and N=2 Moduli

, 2021
11 ...
openaire   +2 more sources

Line defect half-indices of SU(N) Chern-Simons theories

Journal of High Energy Physics
We study the Wilson line defect half-indices of 3d N $$ \mathcal{N} $$ = 2 supersymmetric SU(N) Chern-Simons theories of level k ≤ – N with Neumann boundary conditions for the gauge fields, together with 2d Fermi multiplets and fundamental 3d chiral ...
Tadashi Okazaki, Douglas J. Smith
doaj   +1 more source

Orientation reversal and the Chern-Simons natural boundary

Journal of High Energy Physics
We show that the fundamental property of preservation of relations, underlying resurgent analysis, provides a new perspective on crossing a natural boundary, an important general problem in theoretical and mathematical physics.
Griffen Adams, Ovidiu Costin, Gerald V. Dunne, Sergei Gukov, Oğuz Öner   +4 more
doaj   +1 more source

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Arithmetic properties for Appell–Lerch sums

Ramanujan Journal, 2021
An Appell-Lerch sum is a series of the form \[ AL(x,q,z)=\frac{1}{(q,q/z,q;q)_\infty}\sum_{n=-\infty}^\infty \frac{(-1)^{+1}q^{n(n+1)/2}z^{n+1}}{1-xzq^n}, \] with certain restrictions on \(x\) and \(z\), and where \[ (a_1,a_2,\ldots,a_k;q)_\infty=(a_1;q)_\infty(a_2;q)_\infty\cdots(a_k;q)_\infty \quad \text{and}\quad (a;q)_\infty=\prod_{n=0}^\infty(1-aq^
Ernest Xia, Xia Ernest X W
exaly   +2 more sources

Ranks, cranks for overpartitions and Appell–Lerch sums

Ramanujan Journal, 2021
The purpose of this paper is to dissect the generating functions for the rank and certain cranks of overpartitions mod 4 and 8, and derive identities therefrom. Define the rank of an overpartition to be the largest part of the overpartition, minus its number of parts.
Yao Olivia X M, Olivia X M Yao
exaly   +2 more sources

Generalizations of Mock Theta Functions and Appell–Lerch Sums

Bulletin of the Iranian Mathematical Society, 2023
Mock theta functions have been a continuing source of inspiration and have motivated a tremendous amount of research over a century. Ramanujan named and studied such functions, which can be represented by Eulerian forms, Appell-Lerch sums, Hecke-type double sums, and Fourier coefficients of meromorphic Jacobi forms.
S -P Cui, Nancy Gu, Dazhao Tang
exaly   +3 more sources

Generalizations of some conjectures of Chan on congruences for Appell–Lerch sums

Journal of Mathematical Analysis and Applications, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Olivia X M Yao
exaly   +3 more sources

Two Identities Involving a Mordell Integral and Appell–Lerch Sums

2018
On page 202 in his Lost Notebook, Ramanujan recorded without proofs two modular transformations involving a Mordell integral, q-hypergeometric series, and generalized Lambert series. These two formulas were first proved by Y.-S. Choi [110], and in this chapter we relate his proofs.
George Andrews, Berndt Bruce C, Andrews George E   +2 more
exaly   +2 more sources

Appell–Lerch sums and $$\mathcal {N}=2$$ moduli

Letters in Mathematical Physics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Emile Bouaziz
exaly   +3 more sources