On the summation of some divergent hypergeometric series and related perturbation expansions
Journal of Computational and Applied Mathematics - Special issue on extrapolation and rational approximation
On the kernel of sequence transformations
Applied Numerical Mathematics - Special issue: a festschrift to honor Professor Robert Vichnevetsky on his 65th birthday
A derivation of extrapolation algorithms based on error estimates
Proceedings of the 6th international congress on Computational and applied mathematics
Certain classes of series associated with the Zeta and related functions
Applied Mathematics and Computation - Special issue: Advanced special functions and related topics in differential equations, third Melfi workshop, proceedings of the Melfi school on advanced topics in mathematics and physics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
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Factorial series played a major role in Stirling's classic book Methodus Differentialis (1730), but now only a few specialists still use them. This article wants to show that this neglect is unjustified, and that factorial series are useful numerical tools for the summation of divergent (inverse) power series. This is documented by summing the divergent asymptotic expansion for the exponential integral E"1(z) and the factorially divergent Rayleigh-Schrodinger perturbation expansion for the quartic anharmonic oscillator. Stirling numbers play a key role since they occur as coefficients in expansions of an inverse power in terms of inverse Pochhammer symbols and vice versa. It is shown that the relationships involving Stirling numbers are special cases of more general orthogonal and triangular transformations.