\(k\)-hypergeometric series solutions to one type of non-homogeneous \(k\)-hypergeometric equations. (English) Zbl 1416.33014
Summary: 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.
MSC:
| 33C20 | Generalized hypergeometric series, \({}_pF_q\) |
| 34A30 | Linear ordinary differential equations and systems |
Keywords:
\(k\)-hypergeometric differential equations; non-homogeneous; \(k\)-hypergeometric series; special function; general solution; Frobenius methodReferences:
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