Bernoulli%20and%20Euler%20numbers%20and%20polynomials
(0.005 seconds)
1—10 of 12 matching pages
1: Bibliography L
…
►
An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
►
The real zeros of the Bernoulli polynomials.
J. Approx. Theory 58 (2), pp. 124–150.
…
►
Hermite polynomials in asymptotic representations of generalized Bernoulli, Euler, Bessel, and Buchholz polynomials.
J. Math. Anal. Appl. 239 (2), pp. 457–477.
►
Uniform approximations of Bernoulli and Euler polynomials in terms of hyperbolic functions.
Stud. Appl. Math. 103 (3), pp. 241–258.
…
►
Large degree asymptotics of generalized Bernoulli and Euler polynomials.
J. Math. Anal. Appl. 363 (1), pp. 197–208.
…
2: 25.6 Integer Arguments
3: Bibliography
…
►
On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
►
Congruences of -adic integer order Bernoulli numbers.
J. Number Theory 59 (2), pp. 374–388.
…
►
Some determinants of Bernoulli, Euler and related numbers.
Portugal. Math. 18, pp. 91–99.
…
►
Sharp bounds for the Bernoulli numbers.
Arch. Math. (Basel) 74 (3), pp. 207–211.
…
►
A primer on Bernoulli numbers and polynomials.
Math. Mag. 81 (3), pp. 178–190.
…
4: 24.2 Definitions and Generating Functions
§24.2 Definitions and Generating Functions
►§24.2(i) Bernoulli Numbers and Polynomials
… ►§24.2(ii) Euler Numbers and Polynomials
… ►§24.2(iii) Periodic Bernoulli and Euler Functions
… ► …5: Bibliography F
…
►
…
►
Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
…
►
Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
…
►
Faster computation of Bernoulli numbers.
J. Algorithms 13 (3), pp. 431–445.
…
►
On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
…
6: Software Index
…
►
►
…
►
Software Associated with Books.
…
Open Source | With Book | Commercial | |||||||||||||||||||||||
… | |||||||||||||||||||||||||
20 Theta Functions | |||||||||||||||||||||||||
… | |||||||||||||||||||||||||
24 Bernoulli and Euler Polynomials | |||||||||||||||||||||||||
24.21(ii) , , , | ✓ | ✓ | ✓ | ✓ | a | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | Derive, MuPAD | ||||||||||||
… | |||||||||||||||||||||||||
27 Functions of Number Theory | |||||||||||||||||||||||||
… |
An increasing number of published books have included digital media containing software described in the book. Often, the collection of software covers a fairly broad area. Such software is typically developed by the book author. While it is not professionally packaged, it often provides a useful tool for readers to experiment with the concepts discussed in the book. The software itself is typically not formally supported by its authors.
7: Bibliography K
…
►
Poly-Bernoulli numbers.
J. Théor. Nombres Bordeaux 9 (1), pp. 221–228.
…
►
The congruences of Clausen-von Staudt and Kummer for Bernoulli-Hurwitz numbers.
Math. Ann. 216 (1), pp. 1–4.
…
►
On formulas involving both the Bernoulli and Fibonacci numbers.
Scripta Math. 23, pp. 27–35.
…
►
Remark on -adic -Bernoulli numbers.
Adv. Stud. Contemp. Math. (Pusan) 1, pp. 127–136.
…
►
Computation of tangent, Euler, and Bernoulli numbers.
Math. Comp. 21 (100), pp. 663–688.
…
8: 5.11 Asymptotic Expansions
…
►For the Bernoulli numbers
, see §24.2(i).
…
►Wrench (1968) gives exact values of up to .
…For explicit formulas for in terms of Stirling numbers see Nemes (2013a), and for asymptotic expansions of as see Boyd (1994) and Nemes (2015a).
…
►where is fixed, and is the Bernoulli polynomial defined in §24.2(i).
…
►In terms of generalized Bernoulli polynomials
(§24.16(i)), we have for ,
…
9: Bibliography W
…
►
Prime Divisors of the Bernoulli and Euler Numbers.
In Number Theory for the Millennium, III (Urbana, IL, 2000),
pp. 357–374.
…
►
The zeros of Euler’s psi function and its derivatives.
J. Math. Anal. Appl. 332 (1), pp. 607–616.
…
►
The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
…
►
Generating functions of class-numbers.
Compositio Math. 1, pp. 39–68.
…
►
Hypergeometric Series, Recurrence Relations and Some New Orthogonal Polynomials.
Ph.D. Thesis, University of Wisconsin, Madison, WI.
…
10: Bibliography B
…
►
Character analogues of the Poisson and Euler-MacLaurin summation formulas with applications.
J. Number Theory 7 (4), pp. 413–445.
►
Periodic Bernoulli numbers, summation formulas and applications.
In Theory and Application of Special Functions (Proc. Advanced
Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis.,
1975),
pp. 143–189.
…
►
On the Euler and Bernoulli polynomials.
J. Reine Angew. Math. 234, pp. 45–64.
…
►
Bernoulli polynomials and asymptotic expansions of the quotient of gamma functions.
J. Comput. Appl. Math. 235 (11), pp. 3315–3331.
…
►
Bernoulli numbers and polynomials of arbitrary complex indices.
Appl. Math. Lett. 5 (6), pp. 83–88.
…