Digital Library of Mathematical Functions
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24 Bernoulli and Euler PolynomialsProperties

§24.11 Asymptotic Approximations

As n

24.11.1 (-1)n+1B2n 2(2n)!(2π)2n,
24.11.2 (-1)n+1B2n 4πn(nπ)2n,
24.11.3 (-1)nE2n 22n+2(2n)!π2n+1,
24.11.4 (-1)nE2n 8nπ(4nπ)2n.

Also,

24.11.5 (-1)n/2-1(2π)n2(n!)Bn(x) {cos(2πx),n even,sin(2πx),n odd,
24.11.6 (-1)(n+1)/2πn+14(n!)En(x) {sin(πx),n even,cos(πx),n odd,

uniformly for x on compact subsets of .

For further results see Temme (1995b) and López and Temme (1999b).