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Recurrence relations for the Maclaurin coefficients of products of elementary functions and Hypergeometric functions
Zhong-Xuan Mao, Jing-Feng Tian
In this paper, we investigate the recurrence relations for the Maclaurin coefficients of the products of elementary functions and hypergeometric functions. Specifically, we focus o…
Recurrence Relations for the Maclaurin Coefficients of Products of Elementary Functions and the Bessel Functions
Zhong-Xuan Mao, Jing-Feng Tian
In this paper, we investigate recurrence relations for the Maclaurin coefficients of the products of a elementary function and the Bessel function of the first kind $\mathcal{J}(z)…
Recurrence relations for the coefficients of the confluent and Gauss hypergeometric functions in the complex plane
Zi-Qiao Xu, Zhong-Xuan Mao, Jing-Feng Tian
For , where is the complex plane, , let \begin{equation*} \mathcal{M}\left( z\right) =\left( 1-…
Recurrence relations and applications for the Maclaurin coefficients of squared and cubic hypergeometric functions
Zhong-Xuan Mao, Jing-Feng Tian
In this paper, we present and prove that the coefficients and in the series expansions and $F^3(a,b;c;z) = \sum_{n=0}^\infty…