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Inequalities for hyperbolic functions
Applied Mathematics and Computation, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Edward Neuman, József Sándor
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Advances in Computational Mathematics, 2009
The Gauss error function of a real variable is defined by \(\text{erf}(x)= {2\over\sqrt{\pi}} \int^x_0 e^{-t^2}\,dt\). Results on the error function may be found e.g., in the well-known monographs by Abramowitz-Stegun (1965), Gradshteyn-Ryzhik (1994), or Luke (1975).
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The Gauss error function of a real variable is defined by \(\text{erf}(x)= {2\over\sqrt{\pi}} \int^x_0 e^{-t^2}\,dt\). Results on the error function may be found e.g., in the well-known monographs by Abramowitz-Stegun (1965), Gradshteyn-Ryzhik (1994), or Luke (1975).
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Numerical Algorithms, 2008
Some new inequalities for Euler's gamma function are derived and proved.
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Some new inequalities for Euler's gamma function are derived and proved.
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Inequalities for the Polygamma Functions
SIAM Journal on Mathematical Analysis, 1998Summary: Let \(F_n(x;c)=(\Psi^{(n)}(x))^2-c\Psi^{(n-1)}(x)\Psi^{(n+1)}(x)\) \((x>0)\), where \(\Psi\) denotes the logarithmic derivative of the gamma function, \(n\geq 2\) is an integer, and \(c\) is a real number. The authors prove that the function \(x\mapsto F_n(x;\alpha)\) is strictly completely monotonic on \((0,\infty)\) if and only if \(\alpha ...
Alzer, Horst, Wells, Jim
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