On the Gosper’s q-constant Πq

Mohamed El Bachraoui

doi:10.1007/s10114-018-8019-4

On the Gosper’s q-constant Π_q

Mohamed El Bachraoui

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

Gosper introduced the functions sin_qz and cos_qz as q-analogues for the trigonometric functions sin z and cos z respectively. He stated a variety of identities involving these two q-trigonometric functions along with certain constants denoted by Πqn (n ∈ N). Gosper noticed that all his formulas on these constants have more than two of the Πqn. So, it is natural to raise the question of establishing identities involving only two of the Πqn. In this paper, our main goal is to give examples of such formulas in only two Πqn.

Original language	English
Pages (from-to)	1755-1764
Number of pages	10
Journal	Acta Mathematica Sinica, English Series
Volume	34
Issue number	11
DOIs	https://doi.org/10.1007/s10114-018-8019-4
Publication status	Published - Nov 1 2018

Keywords

11F11
11F12
33E05
elliptic functions
q-trigonometric functions
theta function identities

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1007/s10114-018-8019-4

Cite this

@article{e678cc1c586b490c845621a55bfa35e3,

title = "On the Gosper{\textquoteright}s q-constant Πq ",

abstract = "Gosper introduced the functions sinqz and cosqz as q-analogues for the trigonometric functions sin z and cos z respectively. He stated a variety of identities involving these two q-trigonometric functions along with certain constants denoted by Πqn (n ∈ N). Gosper noticed that all his formulas on these constants have more than two of the Πqn. So, it is natural to raise the question of establishing identities involving only two of the Πqn. In this paper, our main goal is to give examples of such formulas in only two Πqn.",

keywords = "11F11, 11F12, 33E05, elliptic functions, q-trigonometric functions, theta function identities",

author = "{El Bachraoui}, Mohamed",

note = "Publisher Copyright: {\textcopyright} 2018, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2018",

month = nov,

day = "1",

doi = "10.1007/s10114-018-8019-4",

language = "English",

volume = "34",

pages = "1755--1764",

journal = "Acta Mathematica Sinica, English Series",

issn = "1439-8516",

publisher = "Springer Verlag",

number = "11",

}

TY - JOUR

T1 - On the Gosper’s q-constant Πq

AU - El Bachraoui, Mohamed

N1 - Publisher Copyright: © 2018, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2018/11/1

Y1 - 2018/11/1

N2 - Gosper introduced the functions sinqz and cosqz as q-analogues for the trigonometric functions sin z and cos z respectively. He stated a variety of identities involving these two q-trigonometric functions along with certain constants denoted by Πqn (n ∈ N). Gosper noticed that all his formulas on these constants have more than two of the Πqn. So, it is natural to raise the question of establishing identities involving only two of the Πqn. In this paper, our main goal is to give examples of such formulas in only two Πqn.

AB - Gosper introduced the functions sinqz and cosqz as q-analogues for the trigonometric functions sin z and cos z respectively. He stated a variety of identities involving these two q-trigonometric functions along with certain constants denoted by Πqn (n ∈ N). Gosper noticed that all his formulas on these constants have more than two of the Πqn. So, it is natural to raise the question of establishing identities involving only two of the Πqn. In this paper, our main goal is to give examples of such formulas in only two Πqn.

KW - 11F11

KW - 11F12

KW - 33E05

KW - elliptic functions

KW - q-trigonometric functions

KW - theta function identities

UR - http://www.scopus.com/inward/record.url?scp=85048300827&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048300827&partnerID=8YFLogxK

U2 - 10.1007/s10114-018-8019-4

DO - 10.1007/s10114-018-8019-4

M3 - Article

AN - SCOPUS:85048300827

SN - 1439-8516

VL - 34

SP - 1755

EP - 1764

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 11

ER -