Improved \(q\)-exponential and \(q\)-trigonometric functions

DOI10.1016/j.aml.2011.06.009zbMath1232.33025arXiv1006.5652OpenAlexW2963701787MaRDI QIDQ654260

Jan L. Cieśliński

Publication date: 28 December 2011

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.5652

zbMATH Keywords

Cayley transform\(q\)-calculus\(q\)-trigonometric functionsquantum calculus\(q\)-exponential function

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Related Items (13)

On \(q\)-BFGS algorithm for unconstrained optimization problems ⋮ An extended generalized \(q\)-extensions for the Apostol type polynomials ⋮ Hyers-Ulam stability for quantum equations ⋮ On q-analogs of zeta functions associated with a pair of q-analogs of Bernoulli numbers and polynomials ⋮ Unnamed Item ⋮ On a class of \(q\)-Bernoulli, \(q\)-Euler, and \(q\)-Genocchi polynomials ⋮ The sine-Gordon equation on time scales ⋮ New definitions of exponential, hyperbolic and trigonometric functions on time scales ⋮ On basic Fourier-Bessel expansions ⋮ Hyers-Ulam stability for Cayley quantum equations and its application to \(h\)-difference equations ⋮ Some new sums of q-trigonometric and related functions through a theta product of Jacobi ⋮ On the generalized q-poly-Euler polynomials of the second kind ⋮ A new type of q-Szász-Mirakjan operators

Cites Work

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• Disentangling \(q\)-exponentials: a general approach
• Analysis on measure chains - a unified approach to continuous and discrete calculus
• The \(h\)-Laplace and \(q\)-Laplace transforms
• ``Addition theorems for some \(q\)-exponential and \(q\)-trigonometric functions
• On \(q\)-difference equations and \(\mathbb{Z}_n\) decompositions of \(\exp_q\) function
• Method of separation of the variables for basic analogs of equations of mathematical physics
• Another addition theorem for theq-exponential function
• On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)_q
• An example of Feynman–Jackson integrals
• The quantum group SU_q(2) and a q-analogue of the boson operators
• q-UNCERTAINTY RELATIONS
• On a one-parameter family ofq-exponential functions
• On the Fourier - Gauss transforms of someq-exponential andq-trigonometric functions
• qqq-Newton Binomial: From Euler To Gauss
• q-exponential and q-gamma functions. I. q-exponential functionsa)
• A discrete quantum model of the harmonic oscillator
• On Cayley-transform methods for the discretization of Lie-group equations
• Quantum calculus
• Basic analog of Fourier series on a \(q\)-linear grid.

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