On the Atkin polynomials (Q482094)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Atkin polynomials |
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On the Atkin polynomials (English)
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19 December 2014
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The paper is devoted to study the Atkin polynomials, establishing many new properties of this family of polynomials. First the authors present a representation of a scaled version of the Atkin polynomials as a linear combination of associated Jacobi polynomials. As a consequence they deduce an explicit representation of the Atkin polynomials in terms of certain hypergeometric functions and they provide an asymptotic formula and a generating function identity. Finally they give the normalized weight function in terms of hypergeometric functions.
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associated Jacobi polynomials
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asymptotics
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weight functions
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scaled invariant
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modular function
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birth and death process polynomials
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supersingular polynomials
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Hecke operators
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