Bernoulli related polynomials and numbers

Author:
Ch. A. Charalambides

Journal:
Math. Comp. **33** (1979), 794-804

MSC:
Primary 10A40; Secondary 62E15

DOI:
https://doi.org/10.1090/S0025-5718-1979-0521294-5

MathSciNet review:
521294

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Abstract | References | Similar Articles | Additional Information

Abstract: The polynomials of degree *n* defined by the equations

**[1]**J. R. ABERNETHY, "On the elimination of the systematic errors due to grouping,"*Ann. Math. Statist.*, v. 4, 1933, pp. 263-277.**[2]**L. Carlitz,*A degenerate Staudt-Clausen theorem*, Arch. Math. (Basel)**7**(1956), 28–33. MR**0074436**, https://doi.org/10.1007/BF01900520**[3]**Ch. A. Charalambides,*A new kind of numbers appearing in the 𝑛-fold convolution of truncated binomial and negative binomial distributions*, SIAM J. Appl. Math.**33**(1977), no. 2, 279–288. MR**0446989**, https://doi.org/10.1137/0133017**[4]**Ch. A. Charalambides,*Some properties and applications of the differences of the generalized factorials*, SIAM J. Appl. Math.**36**(1979), no. 2, 273–280. MR**524501**, https://doi.org/10.1137/0136022**[5]**F. N. David and D. E. Barton,*Combinatorial chance*, Hafner Publishing Co., New York, 1962. MR**0155371****[6]**C. C. GRAIG, "Sheppard's corrections for a discrete variable,"*Ann. Math. Statist.*, v. 7, 1936, pp. 55-61.**[7]**CH. JORDAN,*Calculus of Finite Differences*, Chelsea, New York, 1960.**[8]**M. G. KENDALL & A. STUART,*The Advanced Theory of Statistics*, Vol. 1, Hafner, New York, 1961.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1979-0521294-5

Keywords:
Difference operator,
generalized factorial,
Stirling polynomials,
Stirling numbers of the first and second kind,
Bernoulli polynomials and numbers of the first and second kind,
generating functions,
probability factorial moments

Article copyright:
© Copyright 1979
American Mathematical Society