Results 41 to 50 of about 27,507 (192)

Hecke-type double sums, Appell-Lerch sums, and mock theta functions (I)

, 2012
By developing a connection between partial theta functions and Appell-Lerch sums, we find and prove a formula which expresses Hecke-type double sums in terms of Appell-Lerch sums and theta functions.
Andrews, Andrews, Andrews, Andrews, Andrews, Appell, Atkin, Berndt, Bringmann, Bringmann, Bruinier, Choi, Choi, Dean R. Hickerson, Eric T. Mortenson, Folsom, Gordon, Griffiths, Hecke, Hickerson, Hickerson, Kac, Kac, Kac, Lerch, McIntosh, Polishchuk, Ramanujan, Rogers, Schilling, Tannery, Watson, Zagier, Zwegers   +33 more
core   +1 more source

Definite Integral Involving Rational Functions of Powers and Exponentials Expressed in Terms of the Lerch Function

Mathematical and Computational Applications, 2021
This paper gives new integrals related to a class of special functions. This paper also showcases the derivation of definite integrals involving the quotient of functions with powers and the exponential function expressed in terms of the Lerch function ...
Robert Reynolds, Allan Stauffer
doaj   +1 more source

Proofs of Some Conjectures of Chan on Appell-Lerch Sums

, 2018
On page 3 of his lost notebook, Ramanujan defines the Appell-Lerch sum $$\phi(q):=\sum_{n=0}^\infty \dfrac{(-q;q)_{2n}q^{n+1}}{(q;q^2)_{n+1}^2},$$ which is connected to some of his sixth order mock theta functions. Let $\sum_{n=1}^\infty a(n)q^n:=\phi(q)$
Baruah, Nayandeep Deka, Begum, Nilufar Mana   +1 more
core   +1 more source

The Lerch zeta function IV. Hecke operators

Research in the Mathematical Sciences, 2016
This paper studies algebraic and analytic structures associated with the Lerch zeta function. It defines a family of two-variable Hecke operators $\{ T_m: \, m \ge 1\}$ given by $T_m(f)(a, c) = \frac{1}{m} \sum_{k=0}^{m-1} f(\frac{a+k}{m}, mc)$ acting on certain spaces of real-analytic functions, including Lerch zeta functions for various parameter ...
Lagarias, Jeffrey C., Li, Wen-Ching Winnie   +1 more
openaire   +3 more sources

Excessive Femoral Anteversion Associated With Worse Clinical Outcomes Following Hip Arthroscopic Surgery and Higher Prevalence of Anteroinferior Labral Tears in Patients With Femoroacetabular Impingement Syndrome

Arthroscopy, EarlyView.
Purpose To compare intraoperative findings associated with instability and clinical outcomes after hip arthroscopic femoroacetabular impingement syndrome (FAIS) surgery in patients with normal anteversion (NA) and excessive femoral anteversion (EA). Methods Inclusion criteria were FAIS cases who underwent primary arthroscopic management from January ...
Yohei Matsushita, Yoichi Murata, Hirotaka Nakashima, Taichi Shimizu, Shinichiro Takada, Keisuke Nakayama, Haruki Nishimura, Hokuto Fukuda, Mitsuru Saito, Akinori Sakai, Soshi Uchida   +10 more
wiley   +1 more source

Sustaining Circular Innovation Under Volatile Market Conditions: The Critical Role of Industry Platforms

Business Strategy and the Environment, EarlyView.
ABSTRACT While industry platforms are widely recognized as enablers of circular innovation, we still know little about how they evolve to scale and sustain innovation as economic conditions tighten and circular economy funding schemes become more selective.
Eva Qi Wang, Julia A. Fehrer, Jonathan J. Baker, Roderick J. Brodie   +3 more
wiley   +1 more source

Approximate functional equations for the Hurwitz and Lerch zeta-functions [PDF]

, 2017
As one of the asymptotic formulas for the zeta-function, Hardy and Littlewood gave asymptotic formulas called the approximate functional equation. In 2003, R. Garunk\v{s}tis, A. Laurin\v{c}ikas, and J.
Miyagawa, Takashi
core   +2 more sources

On the dual nature of partial theta functions and Appell-Lerch sums

, 2014
In recent work, Hickerson and the author demonstrated that it is useful to think of Appell--Lerch sums as partial theta functions. This notion can be used to relate identities involving partial theta functions with identities involving Appell--Lerch sums.
Andrews, Andrews, Andrews, Andrews, Andrews, Andrews, Andrews, Andrews, Andrews, Bailey, Baxter, Bringmann, Choi, Choi, Eric T. Mortenson, Folsom, Hickerson, Hickerson, Lawrence, Lerch, Lovejoy, Mortenson, Ramanujan, Ramanujan, Rhoades, Schur, Slater, Warnaar, Zwegers   +28 more
core   +1 more source

Internationalising the teacher education curriculum: An analysis of syllabi and student experiences

The Curriculum Journal, EarlyView.
Abstract Internationalisation has increasingly become a key dimension of quality in initial teacher education (ITE) programmes. Although it is recognised as a means to strengthen future teachers' competencies and expand their professional knowledge, it remains underdeveloped in practice.
Nafsika Alexiadou, Mai Trang Vu
wiley   +1 more source

A limit theorem for the Lerch zeta-function

Lietuvos Matematikos Rinkinys, 2000
There is not abstract.
Jolita Ignatavičiūtė
doaj   +3 more sources