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Inequalities for Appell Functions
Journal of Mathematical Physics, 1970The asymptotic expansion of one of Appell's generalizations of the Jacobi function is given for one parameter becoming large while the other is kept fixed. Inequalities are given which may be useful when both parameters become large.
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On gamma function inequalities
Scandinavian Actuarial Journal, 1973Watson's method [1] is used to find two convergent monotonically non-decreasing sequences whose upper bounds are equal to Γ(l)Γ(l∓2a)/Γ2(l∓a) ( = K say), provided l > max (0, - 2a). Boyd [2] showed that Gurland's inequality [3] for K corresponds to the first term of the first sequence; Raja Rao's inequality [4] corresponds to the second term of the ...
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Generalized Functional Inequalities
2014The Poincare, logarithmic Sobolev and Sobolev inequalities capture different features of the associated semigroup or the invariant measure, in terms of convergence to equilibrium, estimates on the heat kernels or tail behaviors of the invariant measure. This chapter investigates intermediate or more general families of functional inequalities which are
Dominique Bakry +2 more
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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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2012
As we have mentioned in Chapter 2, the inequalities for differentially subordinated martingales imply related estimates for the square function. However, in general, the inequalities we obtain are not sharp.
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As we have mentioned in Chapter 2, the inequalities for differentially subordinated martingales imply related estimates for the square function. However, in general, the inequalities we obtain are not sharp.
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Functional diferential inequalities
Boletim da Sociedade Brasileira de Matemática, 1978openaire +1 more source