A certain integral-recurrence equation with discrete-continuous auto-convolution. (Q2897393)
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scientific article; zbMATH DE number 6054261
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A certain integral-recurrence equation with discrete-continuous auto-convolution. |
scientific article; zbMATH DE number 6054261 |
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10 July 2012
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integral-recurrence equation
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first order differential recurrence equations
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combinatorial discrete-continuous convolution
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auto-convolution
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Laplace transformable solutions
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0.85334426
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0.8467021
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0.84524053
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0.8446318
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0.84430194
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0.8433887
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0.8400252
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0.8379592
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0.8327051
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A certain integral-recurrence equation with discrete-continuous auto-convolution. (English)
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The author considers the sequence of integral-recurrence equations with the discrete-continuous auto-convolution NEWLINE\[NEWLINE xu_n(x)+\sum _{k=0}^n \int _0^x u_k(t)u_{n-k}(x-t)\, dt=0 NEWLINE\]NEWLINE with \(x\geq 0\) and \(n\in \mathbb {N}\). He shows that under certain additional conditions, the Laplace transformable solutions of the above equation can be computed explicitly and an explicit formula for these solutions is presented. Note that the only essential references in the paper are references to the author's previous papers.
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