Abstract
In this paper, we present a continued fraction approximation for the gamma function. This approximation is fast in comparison with the recently discovered asymptotic series. We also establish the inequalities related to this approximation. Finally, some numerical computations are provided for demonstrating the superiority of our approximation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cao, X.D.: Multiple-correction and continued fraction approximation. J. Math. Anal. Appl. 424, 1425–1446 (2015)
Cao, X.D., You, X.: Multiple-correction and continued fraction approximation (II). Appl. Math. Comput. 261, 192–205 (2015)
Cao, X.D., Xu, H.M., You, X.: Multiple-correction and faster approximation. J. Number Theory 149, 327–350 (2015)
Mortici, C.: Product approximations via asymptotic integration. Am. Math. Mon. 117(5), 434–441 (2010)
Mortici, C.: New improvements of the Stirling formula. Appl. Math. Comput. 217(2), 699–704 (2010)
Mortici, C.: A continued fraction approximation of the gamma function. J. Math. Anal. Appl. 402, 405–410 (2013)
Mortici, C., Srivastava, H.: A product approximation of the gamma function. Numer. Algorithms 69, 595–610 (2015)
Sándor, J., Debnath, L.: On certain inequalities involving the constant e and their applications. J. Math. Anal. Appl. 249, 569–582 (2000)
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No. 61403034), and Beijing Municipal Commission of Education Science and Technology Program KM201510017002. Computations made in this paper were performed using Mathematica 9.0.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
You, X. Continued Fraction Approximation and Inequality of the Gamma Function. Results Math 73, 20 (2018). https://doi.org/10.1007/s00025-018-0797-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00025-018-0797-6