\(k\)-hypergeometric series solutions to one type of non-homogeneous \(k\)-hypergeometric equations (Q2311049)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(k\)-hypergeometric series solutions to one type of non-homogeneous \(k\)-hypergeometric equations |
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\(k\)-hypergeometric series solutions to one type of non-homogeneous \(k\)-hypergeometric equations (English)
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10 July 2019
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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.
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\(k\)-hypergeometric differential equations
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non-homogeneous
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\(k\)-hypergeometric series
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special function
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general solution
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Frobenius method
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