On the asymptotic expansion of the logarithm of Barnes triple gamma function II

Authors

  • Stamatis Koumandos
  • Henrik L. Pedersen

DOI:

https://doi.org/10.7146/math.scand.a-25832

Abstract

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.

Downloads

Published

2017-05-27

How to Cite

Koumandos, S., & Pedersen, H. L. (2017). On the asymptotic expansion of the logarithm of Barnes triple gamma function II. MATHEMATICA SCANDINAVICA, 120(2), 291–304. https://doi.org/10.7146/math.scand.a-25832

Issue

Section

Articles