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.
scientific article; zbMATH DE number 1833069