On the asymptotic expansion of the logarithm of Barnes triple gamma function II
DOI:
https://doi.org/10.7146/math.scand.a-25832Abstract
The remainders in an asymptotic expansion of the logarithm of Barnes triple gamma function give rise to completely monotonic functions of positive order.
References
Anderson, G. D., Vamanamurthy, M. K., and Vuorinen, M., Generalized convexity and inequalities, J. Math. Anal. Appl. 335 (2007), no. 2, 1294–1308. https://doi.org/10.1016/j.jmaa.2007.02.016
Anderson, G. D., Vuorinen, M., and Zhang, X., Topics in special functions III, Analytic number theory, approximation theory, and special functions (Milovanović, G. V. and Rassias, M. T., eds.), Springer, New York, 2014, pp. 297--345.
Baricz, A. and Pogány, T. K., On a sum of modified Bessel functions, Mediterr. J. Math. 11 (2014), no. 2, 349–360. https://doi.org/10.1007/s00009-013-0365-y
Gradshteyn, I. S. and Ryzhik, I. M., Table of integrals, series, and products, fourth ed., Academic Press, New York-London, 1965.
Koumandos, S. and Pedersen, H. L., Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function, J. Math. Anal. Appl. 355 (2009), no. 1, 33–40. https://doi.org/10.1016/j.jmaa.2009.01.042
Koumandos, S. and Pedersen, H. L., On the asymptotic expansion of the logarithm of Barnes triple gamma function, Math. Scand. 105 (2009), no. 2, 287–306. https://doi.org/10.7146/math.scand.a-15119
Koumandos, S. and Pedersen, H. L., On asymptotic expansions of generalized Stieltjes functions, Comput. Methods Funct. Theory 15 (2015), no. 1, 93–115. https://doi.org/10.1007/s40315-014-0094-7
Niculescu, C. P., Convexity according to the geometric mean, Math. Inequal. Appl. 3 (2000), no. 2, 155–167. https://doi.org/10.7153/mia-03-19
Ruijsenaars, S. N. M., On Barnes' multiple zeta and gamma functions, Adv. Math. 156 (2000), no. 1, 107–132. https://doi.org/10.1006/aima.2000.1946
Sokal, A. D., Real-variables characterization of generalized Stieltjes functions, Expo. Math. 28 (2010), no. 2, 179–185. https://doi.org/10.1016/j.exmath.2009.06.004
Widder, D. V., The Laplace Transform, Princeton University Press, Princeton, 1946.
