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Q-Bessel polynomials

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In mathematics, the q-Bessel polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010,14) give a detailed list of their properties.

Definition

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The polynomials are given in terms of basic hypergeometric functions by [1]


Also known as alternative q-Charlier polynomials

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Orthogonality

[2]

where are q-Pochhammer symbols.

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QBessel function abs complex 3D Maple plot
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QBessel function Im complex 3D Maple plot
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QBessel function Re complex 3D Maple plot
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QBessel function abs density Maple plot
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QBessel function Im density Maple plot
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QBessel function Re density Maple plot

References

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