Zeros of Hypergeometric Functions
Copyright policy )Zeros of Hypergeometric Functions
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.
- University of Michigan–Flint United States
- University of Michigan–Ann Arbor United States
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Classical hypergeometric functions, \({}_2F_1\), Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Jacobi polynomials, Euler integral, series, hypergeometric polynomials, hypergeometric functions
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Classical hypergeometric functions, \({}_2F_1\), Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Jacobi polynomials, Euler integral, series, hypergeometric polynomials, hypergeometric functions
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