# Kapteyn inequality

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## 1—10 of 63 matching pages

##### 1: 10.14 Inequalities; Monotonicity
###### Kapteyn’s Inequality
For inequalities for the function $\Gamma\left(\nu+1\right)(2/x)^{\nu}J_{\nu}\left(x\right)$ with $\nu>-\tfrac{1}{2}$ see Neuman (2004). …
##### 3: Edward Neuman
Neuman has published several papers on approximations and expansions, special functions, and mathematical inequalities. …
##### 4: 4.32 Inequalities
###### §4.32 Inequalities
For these and other inequalities involving hyperbolic functions see Mitrinović (1964, pp. 61, 76, 159) and Mitrinović (1970, p. 270).
##### 6: Bibliography Q
• F. Qi and J. Mei (1999) Some inequalities of the incomplete gamma and related functions. Z. Anal. Anwendungen 18 (3), pp. 793–799.
• F. Qi (2008) A new lower bound in the second Kershaw’s double inequality. J. Comput. Appl. Math. 214 (2), pp. 610–616.
• ##### 7: 10.37 Inequalities; Monotonicity
###### §10.37 Inequalities; Monotonicity
For sharper inequalities when the variables are real see Paris (1984) and Laforgia (1991). …
##### 9: 7.8 Inequalities
###### §7.8 Inequalities
7.8.7 $\frac{\sinh x^{2}}{x}<{\mathrm{e}}^{x^{2}}F\left(x\right)=\int_{0}^{x}{\mathrm% {e}}^{t^{2}}\,\mathrm{d}t<\frac{{\mathrm{e}}^{x^{2}}-1}{x},$ $x>0$.
7.8.8 $\operatorname{erf}x<\sqrt{1-{\mathrm{e}}^{-4x^{2}/\pi}},$ $x>0$.
##### 10: 24.9 Inequalities
###### §24.9 Inequalities
Except where otherwise noted, the inequalities in this section hold for $n=1,2,\dotsc$. …