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2019•SymmetryOpen access

k-Hypergeometric Series Solutions to One Type of Non-Homogeneous k-Hypergeometric Equations

Shengfeng Li, Yi Dong

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Abstract

In this paper, we expound on the hypergeometric series solutions for the second-order non-homogeneous k-hypergeometric differential equation with the polynomial term. The general solutions of this equation are obtained in the form of k-hypergeometric series based on the Frobenius method. Lastly, we employ the result of the theorem to find the solutions of several non-homogeneous k-hypergeometric differential equations.

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What this paper is about

In this paper, we expound on the hypergeometric series solutions for the second-order non-homogeneous k-hypergeometric differential equation with the polynomial term. The general solutions of this equation are obtained in the form of k-hypergeometric series based on the Frobenius method. Lastly, we employ the result of the theorem to find the solutions of several non-homogeneous k-hypergeometric differential equations.

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Available abstract

In this paper, we expound on the hypergeometric series solutions for the second-order non-homogeneous k-hypergeometric differential equation with the polynomial term. The general solutions of this equation are obtained in the form of k-hypergeometric series based on the Frobenius method. Lastly, we employ the result of the theorem to find the solutions of several non-homogeneous k-hypergeometric differential equations.

Key concepts: Frobenius solution to the hypergeometric equation, Basic hypergeometric series, Appell series, Confluent hypergeometric function, Hypergeometric function of a matrix argument, Generalized hypergeometric function, Mathematics, Bilateral hypergeometric series

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