Summation formulae for the product of the \(q\)-Kummer functions from \(E_q(2)\) (Q2716246)
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scientific article; zbMATH DE number 1602304
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Summation formulae for the product of the \(q\)-Kummer functions from \(E_q(2)\) |
scientific article; zbMATH DE number 1602304 |
Statements
6 June 2001
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\(q\)-Laguerre functions
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noncommutative plane
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deformed Heisenberg algebra
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Hahn-Exton \(q\)-Vessel functions
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0.8927307
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0.8852953
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0.8839203
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0.87306154
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0.8724277
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0.8685584
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0.8670686
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Summation formulae for the product of the \(q\)-Kummer functions from \(E_q(2)\) (English)
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The authors consider the two-parametric deformation of the plane which is generated by the coordinates \(z\) and \(z^*\) with \(zz^*- qz^*z=\sigma\) with \(q<1\), \(\sigma>0\). Irreducible representations of the associated symmetry group \(E_q(2)\) then lead to formulas for the associated special functions. In particular, summation formulas for certain \(q\)-Kummer functions, and in particular for Hahn-Exton \(q\)-Bessel and \(q\)-Laguerre functions, are obtained in this way.
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