A STUDY ON SOME NEW RESULTS ARISING FROM (p, q)-CALCULUS

被引：0

作者：

Duran, Ugur ^{[1
]}

Acikgoz, Mehmet ^{[2
]}

Araci, Serkan ^{[3
]}

机构：

[1] Iskenderun Tech Univ, Fac Engn & Nat Sci, Dept Basic Concepts Engn, Antakya, Turkey

[2] Gaziantep Univ, Fac Arts & Sci, Dept Math, Gaziantep, Turkey

[3] Hasan Kalyoncu Univ, Fac Econ Adm & Social Sci, Dept Econ, Gaziantep, Turkey

来源：

TWMS JOURNAL OF PURE AND APPLIED MATHEMATICS | 2020年 / 11卷 / 01期

关键词：

q-calculus; (p; q)-calculus; exponential functions; trigonometric functions; hyperbolic functions; Q)-ANALOG; BERNOULLI;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper includes some new investigations and results for post quantum calculus, denoted by (p, q)-calculus. A chain rule for (p, q)-derivative is given. Also, a new (p, q)-analogue of the exponential function is introduced and its properties including the addition property for (p, q)-exponential functions are investigated. Several useful results involving (p, q)binomial co-efficients and (p, q)-antiderivative are discovered. At the final part of this paper, (p, q)-analogue of some elementary functions including trigonometric functions and hyperbolic functions are considered and some properties and relations among them are analyzed extensively.

引用

页码：57 / 71

页数：15

共 25 条

[1]

Acar T, 2016, J INEQUAL APPL, DOI 10.1186/s13660-016-1045-9

[2]

[Anonymous], 2000, HIST Q CALCULUS NEW

[3]

[Anonymous], 2008, ELECT J COMBIN NUMBE

[4] (ρ, q)-Volkenborn integration [J].

Araci, Serkan ;

Duran, Ugur ;

Acikgoz, Mehmet .

JOURNAL OF NUMBER THEORY, 2017, 171 :18-30

[5] FIBONACCI OSCILLATORS [J].

ARIK, M ;

DEMIRCAN, E ;

TURGUT, T ;

EKINCI, L ;

MUNGAN, M .

ZEITSCHRIFT FUR PHYSIK C-PARTICLES AND FIELDS, 1992, 55 (01) :89-95

[6]

Brodimas G., 1991, PREPRINTS

[7]

Burban I.M., 1994, Integral Transform. Spec. Funct, V2, P15, DOI DOI 10.1080/10652469408819035

[8] A (P, Q)-OSCILLATOR REALIZATION OF 2-PARAMETER QUANTUM ALGEBRAS [J].

CHAKRABARTI, R ;

JAGANNATHAN, R .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1991, 24 (13) :L711-L718

[9] A note on the Bernoulli and Euler polynomials [J].

Cheon, GS .

APPLIED MATHEMATICS LETTERS, 2003, 16 (03) :365-368

[10]

Duran U., 2016, J COMPUT THEOR NANOS, V13, P7903, DOI DOI 10.1166/jctn.2016.5790

← 1 2 3 →