Special functions, integral equations and a Riemann-Hilbert problem (Q2817013)
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scientific article; zbMATH DE number 6620002
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Special functions, integral equations and a Riemann-Hilbert problem |
scientific article; zbMATH DE number 6620002 |
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Special functions, integral equations and a Riemann-Hilbert problem (English)
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26 August 2016
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Mittag-Leffler function
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Freud weight
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integral equation
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A vector-matrix boundary value problem with matrix coefficient NEWLINE\[NEWLINE v_L = \left(\begin{aligned} 1 & -\eta_l(s) \\ & \eta_l(s) 1 \end{aligned}\right), NEWLINE\]NEWLINE where \(\eta_L(s) = 2 i (-1)^{n+1} e^{-|s|^\beta \sin \pi \beta/2} \sin\left(|s|^\beta \cos \frac{\pi \beta}{2}\right) \mathbf 1_{[0,\infty)}(s), s\in {\mathbb R}\) is related to two integral equations on the semi-axes with a one-point singularity and a Freud-type weight. The solutions of these equations are represented in terms of a special function of Mittag-Leffler type.
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