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New inequalities for the zeros of confluent hypergeometric functions. (English) Zbl 0701.33006
Asymptotic and computational analysis. Conference in honor of Frank W.J. Olver’s 65th birthday, Proc. Int. Symp., Winnipeg/Can. 1989, Lect. Notes Pure Appl. Math. 124, 175-192 (1990).

[For the entire collection see Zbl 0689.00009.]

The Kummer function ${\Phi }$ (a,c;x) and Tricomi function $\psi$ (a,c;x) are the integrals of the confluent hypergeometric equation

${x}^{2}{y}^{\text{'}\text{'}}+\left(c-x\right){y}^{\text{'}}-ay=0·$

The aim of this paper is to derive bounds for the zeros of the Kummer and Tricomi functions (theorems 2.1, 2.2, 3.1). For this purpose the Sturm comparison theorem is used. The same method, in earlier papers by the author, was applied to obtain inequalities for the zeros of Jacobi and Laguerre polynomials (see references). Numerical results for particular cases are given.

Reviewer: St.Kus
##### MSC:
 33C15 Confluent hypergeometric functions, Whittaker functions, ${}_{1}{F}_{1}$ 34C10 Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory 65D20 Computation of special functions, construction of tables
##### Keywords:
Whittaker function; Kummer function; Tricomi function