Inequalities involving generalized Bessel functions.
On Kaluza's sign criterion for reciprocal power series
T. Kaluza has given a criterion for the signs of the power series of a function that is the reciprocal of another power series. In this note the sharpness of this condition is explored and various examples in terms of the Gaussian hypergeometric series are given. A criterion for the monotonicity of the quotient of two power series due to M. Biernacki and J. Krzyż is applied.
On Kaluza’s sign criterion for reciprocal power series
T. Kaluza has given a criterion for the signs of the power series of a function that is the reciprocal of another power series. In this note the sharpness of this condition is explored and various examples in terms of the Gaussian hypergeometric series are given. A criterion for the monotonicity of the quotient of two power series due to M. Biernacki and J. Krzyż is applied.
Grünbaum-type inequalities for special functions.
Redheffer type inequality for Bessel functions.
Convexity of the zero-balanced Gaussian hypergeometric functions with respect to Hölder means.
A functional inequality for the survival function of the gamma distribution.
Jordan-type inequalities for generalized Bessel functions.
Extension of Oppenheim's problem to Bessel functions.
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