Hecke–Rogers type series representations for infinite products

2021 ◽  
Author(s):  
Ying Zhang ◽  
Wenlong Zhang
Keyword(s):  
Infinite Products ◽  
Type Series ◽  
Series Representations

scholarly journals On some properties of the Lüroth-type alternating series representations for real numbers

2001 ◽  
Vol 28 (6) ◽  
pp. 367-373 ◽  
Author(s):  
C. Ganatsiou
Keyword(s):  
Limit Theorems ◽  
Asymptotic Density ◽  
Real Numbers ◽  
Type Series ◽  
Distribution Of The Maximum ◽  
Series Representations

We investigate some properties connected with the alternating Lüroth-type series representations for real numbers, in terms of the integer digits involved. In particular, we establish the analogous concept of the asymptotic density and the distribution of the maximum of the firstndenominators, by applying appropriate limit theorems.

scholarly journals ON THE q-DERIVATIVE AND q-SERIES EXPANSIONS

2013 ◽  
Vol 09 (08) ◽  
pp. 2069-2089 ◽  
Author(s):  
ZHI-GUO LIU
Keyword(s):  
Series Expansion ◽  
Generating Function ◽  
Series Expansions ◽  
Infinite Products ◽  
Type Series ◽  
Famous Result ◽  
Triangular Numbers

Using a general q-series expansion, we derive some nontrivial q-formulas involving many infinite products. A multitude of Hecke-type series identities are derived. Some general formulas for sums of any number of squares are given. A new representation for the generating function for sums of three triangular numbers is derived, which is slightly different from that of Andrews, also implies the famous result of Gauss where every integer is the sum of three triangular numbers.

scholarly journals New integral and series representations of the generalized Mathieu series

2008 ◽  
Vol 2 (2) ◽  
pp. 205-212 ◽  
Author(s):  
Zivorad Tomovski
Keyword(s):  
Integral Representations ◽  
Type Series ◽  
Fourier Sine ◽  
Series Representations ◽  
Mathieu Series

By using some recently investigated fourier sine integral representations for the Mathieu type series (see [4]), new integral and series representations are derived here for certain general families of Mathieu type series.

Productly linearly independent sequences

2015 ◽  
Vol 52 (3) ◽  
pp. 350-370
Author(s):  
Jaroslav Hančl ◽  
Katarína Korčeková ◽  
Lukáš Novotný
Keyword(s):  
Rational Numbers ◽  
Infinite Products ◽  
Linearly Independent ◽  
New Concepts ◽  
Infinite Sequences

We introduce the two new concepts, productly linearly independent sequences and productly irrational sequences. Then we prove a criterion for which certain infinite sequences of rational numbers are productly linearly independent. As a consequence we obtain a criterion for the irrationality of infinite products and a criterion for a sequence to be productly irrational.

Generalized Kantorovich sampling type series on hypergroups

2018 ◽  
Vol 48 (1) ◽  
pp. 117-127
Author(s):  
Seyyed Mohammad Tabatabaie ◽  
A. Sathish Kumar ◽  
Mahmood Pourgholamhossein
Keyword(s):  
Type Series

First Records of Bufo luchunnicus (Yang et Rao, 2008) and Amolops wenshanensis Yuan, Jin, Li, Stuart et Wu, 2018 (Anura: Bufonidae, Ranidae) from Vietnam

2020 ◽  
Vol 27 (2) ◽  
pp. 81-86
Author(s):  
Cuong The Pham ◽  
Minh Duc Le ◽  
Chung Van Hoang ◽  
Anh Van Pham ◽  
Thomas Ziegler ◽  
...  
Keyword(s):  
Natural History ◽  
Genetic Divergence ◽  
Morphological Data ◽  
Type Series ◽  
Lao Cai ◽  
First Time ◽  
Nd2 Gene ◽  
Quang Ninh

We record two species of amphibians for the first time from Vietnam: Bufo luchunnicus from Lao Cai and Son La provinces and Amolops wenshanensis from Quang Ninh Province. Morphologically, the Vietnamese representatives of B. luchunnicus resemble the type series from China. The specimen of A. wenshanensis from Vietnam slightly differs from the type series from China by having a smaller size (SVL 33.2 mm vs. 35.7 – 39.9 mm in males) and the presence of distinct transverse bands on the dorsal surfaces of limbs. Genetic divergence between the sequence of the Vietnamese specimen and those of A. wenshanensis from China available from GenBank is 1.2 – 1.6% (ND2 gene). In addition, morphological data and natural history notes of aforementioned species are provided from Vietnam.

A general inverse matrix series relation and associated polynomials – II

2021 ◽  
Vol 71 (2) ◽  
pp. 301-316
Author(s):  
Reshma Sanjhira
Keyword(s):  
Matrix Polynomial ◽  
Combinatorial Identities ◽  
Inverse Matrix ◽  
Matrix Polynomials ◽  
Special Cases ◽  
Series Representations ◽  
The Matrix ◽  
Associated Polynomials ◽  
Matrix Pair ◽  
Matrix Series

Abstract We propose a matrix analogue of a general inverse series relation with an objective to introduce the generalized Humbert matrix polynomial, Wilson matrix polynomial, and the Rach matrix polynomial together with their inverse series representations. The matrix polynomials of Kiney, Pincherle, Gegenbauer, Hahn, Meixner-Pollaczek etc. occur as the special cases. It is also shown that the general inverse matrix pair provides the extension to several inverse pairs due to John Riordan [An Introduction to Combinatorial Identities, Wiley, 1968].

scholarly journals A dominated convergence theorem for Eisenstein series

2021 ◽  
Author(s):  
Johann Franke
Keyword(s):  
Fourier Series ◽  
Dirichlet Series ◽  
Eisenstein Series ◽  
Modular Forms ◽  
Convergence Theorem ◽  
Rational Functions ◽  
New Approach ◽  
Series Representations ◽  
Dominated Convergence ◽  
Generalized Dirichlet

AbstractBased on the new approach to modular forms presented in [6] that uses rational functions, we prove a dominated convergence theorem for certain modular forms in the Eisenstein space. It states that certain rearrangements of the Fourier series will converge very fast near the cusp $$\tau = 0$$ τ = 0 . As an application, we consider L-functions associated to products of Eisenstein series and present natural generalized Dirichlet series representations that converge in an expanded half plane.

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