Some new sums of q-trigonometric and related functions through a theta product of Jacobi
نویسندگان
چکیده
منابع مشابه
a contrastive study of rhetorical functions of citation in iranian and international elt scopus journals
writing an academic article requires the researchers to provide support for their works by learning how to cite the works of others. various studies regarding the analysis of citation in m.a theses have been done, while little work has been done on comparison of citations among elt scopus journal articles, and so the dearth of research in this area demands for further investigation into citatio...
q-HYPERGEOMETRIC DOUBLE SUMS AS MOCK THETA FUNCTIONS
Recently, Bringmann and Kane established two new Bailey pairs and used them to relate certain q-hypergeometric series to real quadratic fields. We show how these pairs give rise to new mock theta functions in the form of q-hypergeometric double sums. Additionally, we prove an identity between one of these sums and two classical mock theta functions introduced by Gordon and McIntosh.
متن کاملTrigonometric Identities and Sums of Separable Functions
Modern computers have made commonplace many calculations that were impossible to imagine a few years ago. Still, when you face a problem with a high physical dimension, you immediately encounter the Curse of Dimensionality [1, p.94]. This curse is that the amount of computing power that you need grows exponentially with the dimension. The simplest manifestation of this curse appears when you tr...
متن کاملNew estimates of double trigonometric sums with exponential functions
We establish a new bound for the exponential sum x∈X y∈Y γ(y) exp(2πiaλ xy /p) , where λ is an element of the residue ring modulo a large prime number p, X and Y are arbitrary subsets of the residue ring modulo p − 1 and γ(n) are any complex numbers with |γ(n)| ≤ 1. In particular, we improve several previously known bounds.
متن کاملOn Some Trigonometric Power Sums
In contrast to Fourier series, these finite power sums are over the angles equally dividing the upper-half plane. Moreover, these beautiful and somewhat surprising sums often arise in analysis. In this note, we extend the above results to the power sums as shown in identities (17), (19), (25), (26), (32), (33), (34), (35), and (36) and in the appendix. The method is based on the generating func...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2020
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042120500931