Numbers generated by the reciprocal of

Author:
F. T. Howard

Journal:
Math. Comp. **31** (1977), 581-598

MSC:
Primary 10A40; Secondary 05A17

DOI:
https://doi.org/10.1090/S0025-5718-1977-0439741-4

MathSciNet review:
0439741

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we examine the polynomials and the rational numbers defined by means of

**[1]**J. BRILLHART, "On the Euler and Bernoulli polynomials,"*J. Reine Angew. Math.*, v. 234, 1969, pp. 45-64. MR**39**#4117. MR**0242790 (39:4117)****[2]**L. CARLITZ, "Note on irreducibility of the Bernoulli and Euler polynomials,"*Duke Math. J.*, v. 19, 1952, pp. 475-481. MR**14**, 163. MR**0049381 (14:163h)****[3]**L. CARLITZ, "Note on the numbers of Jordan and Ward,"*Duke Math. J.*, v. 38, 1971, pp. 783-790. MR**45**#1776. MR**0292693 (45:1776)****[4]**L. CARLITZ, "The Staudt-Clausen theorem,"*Math. Mag.*, v. 34, 1960/61, pp. 131-146. MR**24**#A258. MR**0130397 (24:A258)****[5]**L. CARLITZ, "Set partitions,"*Fibonacci Quart.*(To appear.) MR**0427087 (55:123)****[6]**F. T. HOWARD, "A sequence of numbers related to the exponential function,"*Duke Math. J.*, v. 34, 1967, pp. 599-616. MR**36**#130. MR**0217035 (36:130)****[7]**F. T. HOWARD, "Factors and roots of the van der Pol polynomials,"*Proc. Amer. Math. Soc.*, v. 53, 1975, pp. 1-8. MR**52**#252. MR**0379347 (52:252)****[8]**F. T. HOWARD, "Some sequences of rational numbers related to the exponential function,"*Duke Math. J.*, v. 34, 1967, pp. 701-716. MR**36**#131. MR**0217036 (36:131)****[9]**F. T. HOWARD, "Roots of the Euler polynomials,"*Pacific J. Math.*, v. 64, 1976, pp. 181-191. MR**0417394 (54:5444)****[10]**K. INKERI, "The real roots of Bernoulli polynomials,"*Ann. Univ. Turku. Ser. A*I, v. 37, 1959, pp. 3-20. MR**22**#1703. MR**0110835 (22:1703)****[11]**D. JACKSON,*Fourier Series and Orthogonal Polynomials*, Carus Monograph Ser., no. 6, Math. Assoc. of America, Oberlin, Ohio, 1941. MR**3**, 230. MR**0005912 (3:230f)****[12]**C. JORDAN,*Calculus of Finite Differences*, Hungarian Agent Eggenberger Book-Shop, Budapest, 1939; Chelsea, New York, 1950. MR**1**, 74.**[13]**K. KNOPP,*Infinite Sequences and Series*, Dover, New York, 1956. MR**18**, 30. MR**0079110 (18:30c)****[14]**P. A. MacMAHON,*Combinatory Analysis*, Chelsea, New York, 1960. MR**25**#5003. MR**0141605 (25:5003)****[15]**N. E. NÖRLUND,*Vorlesungen über Differenzrechnung*, Springer-Verlag, Berlin, 1924.**[16]**J. RIORDAN,*An Introduction to Combinatorial Analysis*, Chapman & Hall, London; Wiley, New York, 1958. MR**20**#3077. MR**0096594 (20:3077)****[17]**E. C. TITCHMARSH,*The Theory of Functions*, 2nd ed., Oxford, London, 1939.

Retrieve articles in *Mathematics of Computation*
with MSC:
10A40,
05A17

Retrieve articles in all journals with MSC: 10A40, 05A17

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1977-0439741-4

Keywords:
Bernoulli number and polynomial,
Stirling numbers of the second kind,
associated Stirling numbers of the second kind,
Eisenstein's irreducibility criterion,
set partition,
composition,
Staudt-Clausen theorem

Article copyright:
© Copyright 1977
American Mathematical Society