caa a22 4500 388108525 CHVBK 20180307125346.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500027463 doi S0308210500027463 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500027463 Inequalities and monotonicity properties for zeros of Hermite functions [Elektronische Daten] We study the variation of the zeros of the Hermite function Hλ(t) with respect to the positive real variable λ. We show that, for each non-negative integer n, Hλ(t) has exactly n + 1 real zeros when n < λ ≤ n + 1, and that each zero increases from - ∞ to ∞ as λ increases. We establish a formula for the derivative of a zero with respect to the parameter λ; this derivative is a completely monotonic function of λ. By-products include some results on the regular sign behaviour of differences of zeros of Hermite polynomials as well as a proof of some inequalities, related to work of W. K. Hayman and E. L. Ortiz for the largest zero of Hλ(t). Similar results on zeros of certain confluent hypergeometric functions are given too. These specialize to results on the first, second, etc., positive zeros of Hermite polynomials. Copyright © Royal Society of Edinburgh 1999 Elbert Árpád Mathematical Institute, Hungarian Academy of Sciences, POB 127, H-1364 Budapest, Hungary Muldoon Martin E. Department of Mathematics, York University, Toronto, Ontario, Canada, M3J 1P3 Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/1(1999), 57-75 0308-2105 129:1<57 1999 129 PRM https://doi.org/10.1017/S0308210500027463 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500027463 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Elbert Árpád Mathematical Institute, Hungarian Academy of Sciences, POB 127, H-1364 Budapest, Hungary NATIONALLICENCE 700 1- Muldoon Martin E. Department of Mathematics, York University, Toronto, Ontario, Canada, M3J 1P3 NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/1(1999), 57-75 0308-2105 129:1<57 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge