Formulas for factorial

Author:
Francis J. Murray

Journal:
Math. Comp. **39** (1982), 655-662

MSC:
Primary 33A15; Secondary 39A70, 41A60

DOI:
https://doi.org/10.1090/S0025-5718-1982-0669657-1

MathSciNet review:
669657

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Abstract: Burnside's and Stirling's formulas for factorial *N* are special cases of a family of formulas with corresponding asymptotic series given by E. W. Barnes in 1899. An operational procedure for obtaining these formulas and series is presented which yields both convergent and divergent series and error estimates in the latter case. Two formulas of this family have superior accuracy and the geometric mean is better than either.

**[1]**W. Burnside, "A rapidly convergent series for !,"*Messenger Math.*, v. 46, 1917, pp. 157-159.**[2]**Arthur Erdelyi, Wilhelm Magnus, Fritz Oberhettinger & F. G. Tricomi,*Higher Transcendental Functions*, The Bateman Manuscript Project, California Institute of Technology, McGraw-Hill, New York, 1953. MR**0058756 (15:419i)****[3]**Philip Franklin,*A Treatise on Advanced Calculus*, Wiley, New York, 1940; reprint, Dover, New York, 1964. MR**0002571 (2:77f)****[4]**M. J. Lighthill,*An Introduction to Fourier Analysis and Generalized Functions*, Cambridge Univ. Press, New York, 1960. MR**0115085 (22:5888)****[5]**Kenneth S. Miller,*An Introduction to the Calculus of Finite Differences and Difference Equations*, Holt, New York, 1960; reprint, Dover, New York, 1966. MR**0206540 (34:6358)****[6]**J. R. Wilton, "A proof of Burnside's formula for and certain allied properties of the Riemann -function,"*Messenger Math.*, v. 52, 1922, pp. 90-95.

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DOI:
https://doi.org/10.1090/S0025-5718-1982-0669657-1

Article copyright:
© Copyright 1982
American Mathematical Society