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 ...
Anderson and Qiu (1997) conjectured that the function log Γ (x+1)/x log x is concave for x > 1. In this paper we prove this conjecture. We also study the monotonicity of some functions connected with ...
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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