We define the incomplete gamma function ratio for positive N by \begin{align*}\tag{1}P(N, b, X) &= \int^X_0 t^{N-1}e^{-bt} dt/ \int^\infty_0 t^{N-1}e^{-bt} dt ...
Proceedings of the American Mathematical Society, Vol. 135, No. 11 (Nov., 2007), pp. 3641-3648 (8 pages) Let α > 0 and 0 < c ≠1 be real numbers. The inequality ...
Special functions occupy a central role in mathematical analysis, bridging pure theory and practical application across diverse scientific fields. Their intrinsic properties—such as recurrence ...
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