Asymptotic zero distribution of a class of 3F2 hypergeometric functions

AbstractWe study the asymptotic behavior of the zeros of certain families of 3F2 functions. Classical tools are used to analyse the asymptotic behavior of the zeros of the polynomial 3F2(−n, n+1, 12b+n+1, 1−b−n;z) In addition, families of 3F2 functions that are connected in a formulaic sense with Gauss hypergeometric polynomials of the form 2F1(−n, kn+1kn+2;z), k > 0 and 2F1(−n,b−2n;z) b > 0 are investigated. Numerical evidence of the clustering o zeros on certain curves is generated by Mathematica