Abramowitz, Milton (ed.); Stegun, Irene A. (ed.) Handbook of mathematical functions with formulas, graphs, and mathematical tables. Reprint of the 1972 ed. (English) Zbl 0643.33001 A Wiley-Interscience Publication. Selected Government Publications. New York: John Wiley & Sons, Inc; Washington, D.C.: National Bureau of Standards. xiv, 1046 pp.; $ 44.95 (1984). See the review of the original English edition in Zbl 0171.38503. Cited in 8 ReviewsCited in 113 Documents MSC: 33-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to special functions 00A20 Dictionaries and other general reference works 00A22 Formularies 65A05 Tables in numerical analysis 65Dxx Numerical approximation and computational geometry (primarily algorithms) 41A55 Approximate quadratures 62Q05 Statistical tables 44A10 Laplace transform 11B68 Bernoulli and Euler numbers and polynomials 11M06 \(\zeta (s)\) and \(L(s, \chi)\) 11Y70 Values of arithmetic functions; tables Keywords:handbook; special functions; numerical analysis; tables; gamma function; error integral; Fresnel integral; Legendre functions; Bessel functions; Bessel integrals; Struve functions; hypergeometric functions; confluent hypergeometric functions; parabolic cylindrical functions; Bernoulli polynomials; Euler polynomials; combinatorics; number-theoretic functions; Riemann zeta-function Citations:Zbl 0171.38503; Zbl 0543.33001 PDFBibTeX XML Online Encyclopedia of Integer Sequences: k appears partition(k) times. Triangle T(n,k) read by rows: product of the compositorial weight of the k-th partition of n times A074664(.) applied to each part. Triangle T(n,m) of the coefficients JacobiDC(x,y) = sum_{n>=0} sum_{m=0..n} (-1)^m* T(n,m) *x^(2*n) *y^(2*m)/(2*n)!. Triangle T(n,m) of the coefficients JacobiNC(x,y) = sum_{n>0} sum_{m=0..n-1} (-1)^m* T(n,m) *x^(2*n) *y^(2*m)/(2*n)!. Numerator of E(2*n-1,n), where E(n,x) is the Euler polynomial. a(n) = 1/2*((-1)^n*E(2*n-1,n) - E(2*n-1,0)), where E(n,x) is the Euler polynomial. a(n) = E(2n,n)/2, where E(n,x) is the Euler polynomial. a(1) = 1, for n>=2, a(n) = B(2*n-1, n), where B(n, x) is the Bernoulli polynomial.