Kapteyn inequality

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11: 4.5 Inequalities

§4.5 Inequalities

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§4.5(i) Logarithms

… ►For more inequalities involving the logarithm function see Mitrinović (1964, pp. 75–77), Mitrinović (1970, pp. 272–276), and Bullen (1998, pp. 159–160). ►

§4.5(ii) Exponentials

… ►(When $x=0$ the inequalities become equalities.) …

12: 4.18 Inequalities

§4.18 Inequalities

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Jordan’s Inequality

… ►For more inequalities see Mitrinović (1964, pp. 101–111), Mitrinović (1970, pp. 235–265), and Bullen (1998, pp. 250–254).

13: 5.6 Inequalities

§5.6 Inequalities

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Gautschi’s Inequality

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Kershaw’s Inequality

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14: 19.24 Inequalities

§19.24 Inequalities

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§19.24(i) Complete Integrals

… ►Other inequalities can be obtained by applying Carlson (1966, Theorems 2 and 3) to (19.16.20)–(19.16.23). … ► ►

§19.24(ii) Incomplete Integrals

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15: Donald St. P. Richards

… ►Richards has published numerous papers on special functions of matrix argument, harmonic analysis, multivariate statistical analysis, probability inequalities, and applied probability. …

16: 13.22 Zeros

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17: Richard A. Askey

… ►Another significant contribution was the Askey-Gasper inequality for Jacobi polynomials which was published in Positive Jacobi polynomial sums. II (with G. …This inequality was a key element of Louis de Branges’ proof of the Bieberbach conjecture in 1985. …

18: 19.9 Inequalities

§19.9 Inequalities

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§19.9(i) Complete Integrals

… ►Other inequalities are: … ►

§19.9(ii) Incomplete Integrals

… ►Simple inequalities for incomplete integrals follow directly from the defining integrals (§19.2(ii)) together with (19.6.12): …

19: 8.10 Inequalities

§8.10 Inequalities

… ►The inequalities in (8.10.1) and (8.10.2) are reversed when $a\ge 1$. …For further inequalities of these types see Qi and Mei (1999) and Neuman (2013). …

20: 16.23 Mathematical Applications

… ►In the proof of this conjecture de Branges (1985) uses the inequality …The proof of this inequality is given in Askey and Gasper (1976). …