Geodesic
ON A CONVEXITY THEOREM OF RUSKAI AND WERNER AND RELATED RESULTS
Glasgow mathematical journal, Tome 47 (2005) no. 3, pp. 425-438

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DOI

We show that the function \[ V_q(x)=\frac{2e^{x^2}}{\Gamma(q+1)}\int_{x}^{\infty}e^{-t^2}(t^2-x^2)^qdt\quad{(-1<q\in\mathbf{R}; 0<x\in \mathbf{R})}, \] which has applications in the study of atoms in magnetic fields, satisfies certain monotonicity and convexity properties as well as inequalities. In particular, we prove that $1/V_q$ is convex on $(0,\infty)$ if and only if $q\geq 0$. This extends a recent result of M. B. Ruskai and E. Werner, who established the convexity for all integers $q\geq 0$.
DOI : 10.1017/S0017089505002685
Mots-clés : 33E20, 26D15 
ALZER, HORST. ON A CONVEXITY THEOREM OF RUSKAI AND WERNER AND RELATED RESULTS. Glasgow mathematical journal, Tome 47 (2005) no. 3, pp. 425-438. doi: 10.1017/S0017089505002685
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     title = {ON {A} {CONVEXITY} {THEOREM} {OF} {RUSKAI} {AND} {WERNER} {AND} {RELATED} {RESULTS}},
     journal = {Glasgow mathematical journal},
     pages = {425--438},
     year = {2005},
     volume = {47},
     number = {3},
     doi = {10.1017/S0017089505002685},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089505002685/}
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