Stirling's approximation and a hidden link between two of Ramanujan's approximations

[1]  C. O'Sullivan,et al.  Ramanujan’s approximation to the exponential function and generalizations , 2022, The Ramanujan Journal.

[2]  C. O’Sullivan.  De Moivre and Bell polynomials , 2022, Expositiones Mathematicae.

[3]  S. Finch.  The On-Line Encyclopedia of Integer Sequences , 2021, The Mathematical Intelligencer.

[4]  Amy M. Fu.  Some Identities Related to the Second-Order Eulerian Numbers , 2021, 2104.09316.

[5]  SPECIAL FUNCTIONS , 2021, Water‐Quality Engineering in Natural Systems.

[6]  Grzegorz Rzadkowski,et al.  Some applications of the generalized Eulerian numbers , 2019, J. Comb. Theory, Ser. A.

[7]  Ira M. Gessel,et al.  Lagrange inversion , 2016, J. Comb. Theory, Ser. A.

[8]  Miguel A. Méndez,et al.  The asymptotic expansion for n! and the Lagrange inversion formula , 2011 .

[9]  GergHo Nemes,et al.  On the Coefficients of the Asymptotic Expansion of n , 2010, 1003.2907.

[10]  H. Volkmer.  Factorial series connected with the Lambert function, and a problem posed by Ramanujan , 2008 .

[11]  N. J. A. Sloane,et al.  The On-Line Encyclopedia of Integer Sequences , 2003, Electron. J. Comb..

[12]  Daniel W. Lozier,et al.  NIST Digital Library of Mathematical Functions , 2003, Annals of Mathematics and Artificial Intelligence.

[13]  E. A. Karatsuba,et al.  On the asymptotic representation of the Euler gamma function by Ramanujan , 2001 .

[14]  Masanobu Kaneko,et al.  The Akiyama-Tanigawa algorithm for Bernoulli numbers , 2000 .

[15]  B. Berndt.  Ramanujan’s Notebooks: Part V , 1997 .

[16]  G. Marsaglia,et al.  A new derivation of Stirling's approximation of n ! , 1990 .

[17]  John Marsaglia.  C249. The incomplete gamma function and ramanujan’s rational approximation to e x , 1986 .

[18]  B. Berndt.  Ramanujan's Notebooks , 1985 .

[19]  F. Olver.  Asymptotics and Special Functions , 1974 .

[20]  J. Wrench,et al.  Concerning Two Series for the Gamma Function , 1968 .

[21]  L. Comtet,et al.  Advanced Combinatorics: The Art of Finite and Infinite Expansions , 1974 .

[22]  G. N. Watson.  Theorems Stated by Ramanujan (V): Appronimations Connected with cx , 1929 .