WoS İndeksli Yayınlar Koleksiyonu

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Browsing WoS İndeksli Yayınlar Koleksiyonu by Subject "(Q, h)-Analytic Functions"

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    Citation - WoS: 6
    Citation - Scopus: 7
    Gauss's Binomial Formula and Additive Property of Exponential Functions on T(q-h)
    (UNIV NIS FAC SCI MATH, 2021) Burcu Silindir; Ahmet Yantir; Silindir, Burcu; Yantir, Ahmet
    In this article we focus our attention on (q h)-Gauss's binomial formula from which we discover the additive property of (q h)-exponential functions. We state the (q h)-analogue of Gauss's binomial formula in terms of proper polynomials on T-(qT-h) which own essential properties similar to ordinary polynomials. We present (q h)-Taylor series and analyze the conditions for its convergence. We introduce a new (q h)-analytic exponential function which admits the additive property. As consequences we study (q h)-hyperbolic functions (q h)-trigonometric functions and their significant properties such as (q h)-Pythagorean Theorem and double-angle formulas. Finally we illustrate our results by a first order (q h)-difference equation (q h)-analogues of dynamic diffusion equation and Burger's equation. Introducing (q h)-Hopf-Cole transformation we obtain (q h)-shock soliton solutions of Burger's equation.
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    Citation - WoS: 3
    Citation - Scopus: 3
    Power function and binomial series on T(q-h)
    (TAYLOR & FRANCIS LTD, 2023) Secil Gergun; Burcu Silindir; Ahmet Yantir; Gergün, Seçil; Silindir, Burcu; Yantir, Ahmet
    This article is devoted to present (q h) -analogue of power function which satisfies additivity and derivative properties similar to the ordinary power function. In the light of nabla (q h) -power function we present (q h)-analogue of binomial series and conclude that such power function is (q h)-analytic. We prove the analyticity by showing that both the power function and its absolutely convergent Taylor series solve the same IVP. Finally we present the reductions of (q h)-binomial series to classical binomial series Gauss' binomial and Newton's binomial formulas.