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- W1658005718 abstract "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_alpha(z) when alpha ge -1, confluent hypergeometric functions {}_0F_1(c; z) when c > 0 or 0 > c > -1, Laguerre polynomials L_n^alpha(z) when alpha ge -2, Jacobi polynomials P_n^{(alpha,beta)}(z) when alpha ge -1 and beta 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. Milojevi'c and C. V. Stanojevi'c, 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 P'olya Xi^*(z) function, the K_{iz}(a) functions when a > 0, and some other entire functions." @default.
- W1658005718 created "2016-06-24" @default.
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- W1658005718 date "2008-01-19" @default.
- W1658005718 modified "2023-09-27" @default.
- W1658005718 title "Using integrals of squares of certain real-valued special functions to prove that the Pólya Xi^*(z) function, the functions K_{iz}(a), a > 0, and some other entire functions have only real zeros" @default.
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