Some new inequalities for the gamma, beta and zeta functions. (English) Zbl 1182.33005

Mercer, A. McD.

JIPAM, J. Inequal. Pure Appl. Math. 7, No. 1, Paper No. 29, 6 p. (2006).

Summary: An inequality involving a positive linear operator acting on the composition of two continuous functions is presented. This inequality leads to new inequalities involving the beta, gamma and zeta functions and a large family of functions which are Mellin transforms.

MSC:

33B15	Gamma, beta and polygamma functions
26D07	Inequalities involving other types of functions
39B62	Functional inequalities, including subadditivity, convexity, etc.

Keywords:

gamma functions; beta functions; zeta functions; Mellin transforms