Absolutely monotonic functions related to Euler's gamma function and Barnes' double and triple gamma function

作者：Koumandos Stamatis; Pedersen Henrik L^*

来源：Monatshefte fur Mathematik, 2011, 163(1): 51-69.

DOI：10.1007/s00605-010-0197-9

• Double gamma function
• Triple gamma function
• Asymptotic expansion
• Absolute monotonicity

It is shown that the remainders in asymptotic expansions of the logarithm of Barnes double and triple gamma function and Euler's gamma function are Laplace transformations of positive multiples of absolutely monotonic functions. Applications concerning positivity of sums involving Bernoulli numbers are given.

• 出版日期2011-5