Factorial series connected with the Lambert function, and a problem posed by Ramanujan

DOI10.1007/s11139-007-9104-yzbMath1148.33020OpenAlexW2002240182MaRDI QIDQ954790

Hans W. Volkmer

Publication date: 18 November 2008

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-007-9104-y

zbMATH Keywords

gamma functionfactorial seriesLambert functionRamanujan's conjecture

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Other functions defined by series and integrals (33E20)

Related Items

On geometric properties of the generating function for the Ramanujan sequence, Ramanujan's approximation to the exponential function and generalizations, The median of gamma distribution and a related Ramanujan sequence, The asymptotic expansion for \(n!\) and the Lagrange inversion formula, Stirling's approximation and a hidden link between two of Ramanujan's approximations, A Bernstein function related to Ramanujan's approximations of \(\exp(n)\), The Euler characteristic of out \((F_n)\), Ramanujan's estimate for the gamma function via monotonicity arguments

Cites Work

• On the Lambert \(w\) function
• Error bounds for the Laplace approximation for definite integrals
• A New Derivation of Stirling's Approximation to n!
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