A new continued fraction approximation and inequalities for the Gamma function via the Tri-gamma function
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The main objective of this paper is to propose a product approximation for the Gamma function in the form of continued fraction, via the Tri-gamma function. The importance of this new formula is that the convergence of the corresponding asymptotic series is faster than other recently discovered asymptotic series, and some new inequalities related to the new formula are also established.
KeywordsContinued fraction Approximation Rate of convergence Inequalities Gamma function
Mathematics Subject Classification11J70 33B15 41A25 26D15 41A10
Part of the research was done in the Department of Statistics, The Chinese University of Hong Kong. The first author would like to thank Professor Qi-Man Shao and the staff for their hospitality for providing excellent academic and living environments.