Numbers generated by the reciprocal of

Author:
F. T. Howard

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

MSC:
Primary 10A40; Secondary 05A17

MathSciNet review:
0439741

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

**[1]**John Brillhart,*On the Euler and Bernoulli polynomials*, J. Reine Angew. Math.**234**(1969), 45–64. MR**0242790****[2]**L. Carlitz,*Note on irreducibility of the Bernoulli and Euler polynomials*, Duke Math. J.**19**(1952), 475–481. MR**0049381****[3]**L. Carlitz,*Note on the numbers of Jordan and Ward*, Duke Math. J.**38**(1971), 783–790. MR**0292693****[4]**L. Carlitz,*The Staudt-Clausen theorem*, Math. Mag.**34**(1960/1961), 131–146. MR**0130397****[5]**L. Carlitz,*Set partitions*, Fibonacci Quart.**14**(1976), no. 4, 327–342. MR**0427087****[6]**F. T. Howard,*A sequence of numbers related to the exponential function*, Duke Math. J.**34**(1967), 599–615. MR**0217035****[7]**F. T. Howard,*Factors and roots of the van der Pol polynomials*, Proc. Amer. Math. Soc.**53**(1975), no. 1, 1–8. MR**0379347**, 10.1090/S0002-9939-1975-0379347-9**[8]**F. T. Howard,*Some sequences of rational numbers related to the exponential function*, Duke Math. J.**34**(1967), 701–716. MR**0217036****[9]**F. T. Howard,*Roots of the Euler polynomials*, Pacific J. Math.**64**(1976), no. 1, 181–191. MR**0417394****[10]**K. Inkeri,*The real roots of Bernoulli polynomials*, Ann. Univ. Turku. Ser. A I**37**(1959), 20. MR**0110835****[11]**Dunham Jackson,*Fourier Series and Orthogonal Polynomials*, Carus Monograph Series, no. 6, Mathematical Association of America, Oberlin, Ohio, 1941. MR**0005912****[12]**C. JORDAN,*Calculus of Finite Differences*, Hungarian Agent Eggenberger Book-Shop, Budapest, 1939; Chelsea, New York, 1950. MR**1**, 74.**[13]**Konrad Knopp,*Infinite sequences and series*, Dover Publications, Inc., New York, 1956. Translated by Frederick Bagemihl. MR**0079110****[14]**Percy A. MacMahon,*Combinatory analysis*, Two volumes (bound as one), Chelsea Publishing Co., New York, 1960. MR**0141605****[15]**N. E. NÖRLUND,*Vorlesungen über Differenzrechnung*, Springer-Verlag, Berlin, 1924.**[16]**John Riordan,*An introduction to combinatorial analysis*, Wiley Publications in Mathematical Statistics, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR**0096594****[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:
http://dx.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