Abstract
The aim of this paper is to improve some approximation formulas of Ramanujan type discussed by E.A. Karatsuba [J. Comput. Appl. Math. 135 (2001), 225–240].
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Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards, Applied Mathematical Series, vol. 55. Dover, New York (1972). 9th printing
Anderson, G.D., Vamanamurthy, M.K., Vuorinen, M.: Conformal Invariants, Inequalities, and Quasiconformal Maps, Can. Math. Soc., Ser. Mon. Adv. Txt. Wiley, New York (1997)
Berndt, B.C., Choi, Y.-S., Kang, S.-Y.: The problems submitted by Ramanujan. Contemp. Math. 236, 15–56 (1999)
Gosper, R.W.: Decision procedure for indefinite hypergeometric summation. Proc. Natl. Acad. Sci. USA 75, 40–42 (1978)
Karatsuba, E.A.: On the asymptotic representation of the Euler gamma function by Ramanujan. J. Comput. Appl. Math. 135, 225–240 (2001)
Mortici, C.: A coincidence degree for bifurcation problems. Nonlinear Anal. 53(5), 715–721 (2003)
Mortici, C.: An ultimate extremely accurate formula for approximation of the factorial function. Arch. Math. (Basel) 93(1), 37–45 (2009)
Mortici, C.: Completely monotonic functions associated with gamma function and applications. Carpath. J. Math. 25(2), 186–191 (2009)
Mortici, C.: Product approximations via asymptotic integration. Am. Math. Mon. 117(5), 434–441 (2010)
Mortici, C.: New approximations of the gamma function in terms of the digamma function. Appl. Math. Lett. 23(1), 97–100 (2010)
Mortici, C.: Asymptotic expansions of the generalized Stirling approximation. Math. Comput. Model. 52(9–10), 1867–1868 (2010)
Mortici, C.: The proof of Muqattash–Yahdi conjecture. Math. Comput. Model. 51(9–10), 1154–1159 (2010)
Mortici, C.: Monotonicity properties of the volume of the unit ball in ℝn. Optim. Lett. 4(3), 457–464 (2010)
Mortici, C.: Sharp inequalities related to Gosper’s formula. C. R. Math. Acad. Sci. Paris 348(3–4), 137–140 (2010)
Mortici, C.: A class of integral approximations for the factorial function. Comput. Math. Appl. 59(6), 2053–2058 (2010)
Mortici, C.: Best estimates of the generalized Stirling formula. Appl. Math. Comput. 215(11), 4044–4048 (2010)
Mortici, C.: Very accurate estimates of the polygamma functions. Asymptot. Anal. 68(3), 125–134 (2010)
Mortici, C.: Improved convergence towards generalized Euler–Mascheroni constant. Appl. Math. Comput. 215(9), 3443–3448 (2010)
Mortici, C.: A quicker convergence toward the γ constant with the logarithm term involving the constant e. Carpath. J. Math. 26(1), 86–91 (2010)
Mortici, C.: Optimizing the rate of convergence in some new classes of sequences convergent to Euler’s constant. Anal. Appl. 8(1), 99–107 (2010)
O’Connor, J., Robertson, E.F.: James Stirling. MacTutor History of Mathematics Archive
Ramanujan, S.: The Lost Notebook and Other Unpublished Papers. Narosa, Springer, New Delhi, Berlin (1988). Intr. by G.E. Andrews
Stirling, J.: Methodus differentialis, sive tractatus de summation et interpolation serierum infinitarium. London (1730). English translation by J. Holliday, The Differential Method: A Treatise of the Summation and Interpolation of Infinite Series
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Mortici, C. On Ramanujan’s large argument formula for the Gamma function. Ramanujan J 26, 185–192 (2011). https://doi.org/10.1007/s11139-010-9281-y
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DOI: https://doi.org/10.1007/s11139-010-9281-y