Zeros of hypergeometric functions (Q1848431)
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scientific article; zbMATH DE number 1833069
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Zeros of hypergeometric functions |
scientific article; zbMATH DE number 1833069 |
Statements
Zeros of hypergeometric functions (English)
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1 May 2003
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Here it is shown that the hypergeometric function \(F(a,b;b+1;z)\) has no zeros in a specified half-plane for certain ranges of parameters. It is also shown that the zeros of the hypergeometric polynomials \(F(-n,kn+ \ell+1; kn+ \ell+2;z)\) cluster on one loop of a specified lemniscate. Other results then follow from quadratic relations.
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hypergeometric functions
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hypergeometric polynomials
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Jacobi polynomials
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series
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Euler integral
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0.94892514
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0.93162525
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0.92230844
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0.9213605
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0.91770697
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0.9171404
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0.91712624
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