Using integrals of squares of certain real-valued special functions to prove that the Pólya Ξ^*(z) function, the functions K_{iz}(a), a > 0, and some other entire functions have only real zeros
| dc.creator | Gasper, George | |
| dc.date | 2008-01-19 | |
| dc.date.accessioned | 2026-07-07T08:55:28Z | |
| dc.date.available | 2026-07-07T08:55:28Z | |
| dc.description | Analogous to the use of sums of squares of certain real-valued special functions to prove the reality of the zeros of the Bessel functions J_α(z) when α\ge -1, confluent hypergeometric functions {}_0F_1(c; z) when c > 0 or 0 > c > -1, Laguerre polynomials L_n^α(z) when α\ge -2, Jacobi polynomials P_n^{(α,β)}(z) when α\ge -1 and β\ge -1, and some other entire special functions considered in G. Gasper [Using sums of squares to prove that certain entire functions have only real zeros, in Fourier Analysis: Analytic and Geometric Aspects, W. O. Bray, P. S. Milojević and C. V. Stanojević, eds., Marcel Dekker, Inc., 1994, 171--186.], integrals of squares of certain real-valued special functions are used to prove the reality of the zeros of the Pólya Ξ^*(z) function, the K_{iz}(a) functions when a > 0, and some other entire functions. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/0801.2996 | |
| dc.identifier | http://arxiv.org/abs/0801.2996 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146284 | |
| dc.subject | Complex Variables | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 15A09; 33D15; 33E20 | |
| dc.title | Using integrals of squares of certain real-valued special functions to prove that the Pólya Ξ^*(z) function, the functions K_{iz}(a), a > 0, and some other entire functions have only real zeros | |
| dc.type | text |