Kapteyn%20inequality
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1: 10.14 Inequalities; Monotonicity
§10.14 Inequalities; Monotonicity
… ►Kapteyn’s Inequality
… ►For inequalities for the function with see Neuman (2004). …2: 7.8 Inequalities
3: 20 Theta Functions
Chapter 20 Theta Functions
…4: Bibliography N
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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Inequalities involving Bessel functions of the first kind.
JIPAM. J. Inequal. Pure Appl. Math. 5 (4), pp. Article 94, 4 pp. (electronic).
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Inequalities and bounds for the incomplete gamma function.
Results Math. 63 (3-4), pp. 1209–1214.
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An extension of Turán’s inequality.
Math. Inequal. Appl. 18 (1), pp. 321–335.
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5: 1.7 Inequalities
§1.7 Inequalities
… ►Cauchy–Schwarz Inequality
… ►Minkowski’s Inequality
… ►Cauchy–Schwarz Inequality
… ►§1.7(iv) Jensen’s Inequality
…6: Edward Neuman
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►Neuman has published several papers on approximations and expansions, special functions, and mathematical inequalities.
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7: Bibliography
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Monotonicity theorems and inequalities for the complete elliptic integrals.
J. Comput. Appl. Math. 172 (2), pp. 289–312.
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A harmonic mean inequality for the gamma function.
J. Comput. Appl. Math. 87 (2), pp. 195–198.
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On some inequalities for the incomplete gamma function.
Math. Comp. 66 (218), pp. 771–778.
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Gamma function inequalities.
Numer. Algorithms 49 (1-4), pp. 53–84.
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Inequalities for elliptic integrals.
Publ. Inst. Math. (Beograd) (N.S.) 37(51), pp. 61–63.
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8: 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).9: Bibliography G
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An inequality of Turán type for Jacobi polynomials.
Proc. Amer. Math. Soc. 32, pp. 435–439.
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New inequalities for the zeros of Jacobi polynomials.
SIAM J. Math. Anal. 18 (6), pp. 1549–1562.
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New inequalities for the zeros of confluent hypergeometric functions.
In Asymptotic and computational analysis (Winnipeg, MB, 1989),
pp. 175–192.
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Inequalities for modified Bessel functions and their integrals.
J. Math. Anal. Appl. 420 (1), pp. 373–386.
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A harmonic mean inequality for the gamma function.
SIAM J. Math. Anal. 5 (2), pp. 278–281.
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