Two integrals arising in inverse scattering theory (Q1342355)
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scientific article; zbMATH DE number 710334
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two integrals arising in inverse scattering theory |
scientific article; zbMATH DE number 710334 |
Statements
Two integrals arising in inverse scattering theory (English)
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7 August 1995
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The integral of \(J^ 2_ \nu (xb) {}_ 3F_ 2 (3/2, \mu/2, \mu/2+ 1/2; 1-\nu, 1+\nu; -4b^ 2)b\) over \(b\) from zero to infinity equals \(- \nu x^{\mu-2} \exp (-x)/ 2\Gamma (\mu)\). The integral of \(J^ 2_ \nu (xb) {}_ 2F_ 2 (3/2, \mu/2; 1-\nu, 1+\nu; -b^ 2)b\) over \(b\) from zero to infinity equals \(-\nu x^{\mu-2} \exp (-x^ 2)/ \Gamma(\mu/ 2)\). Here, \(\mu>1\), \(\nu\geq 1/2\).
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Bessel function
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generalized hypergeometric series
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confluent hypergeometric function
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0.92749834
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0.90297943
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0.90282583
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0.90234476
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0.90202665
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0.9005642
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