OFFSET
0,2
COMMENTS
arcsinh(cos(x)*tan(x)) = x - 2/3!*x^3 + 20/5!*x^5 - 632/7!*x^7 + 39440/9!*x^9...
arcsin(sinh(x)) = x + 2*x^3/3! + 20*x^5/5! + 620*x^7/7! +...
arccosh(sin(x)) = Pi/2 - x + 2*x^3/3! - 20*x^5/5! + 620*x^7/7! -...
LINKS
Nikolay Sh. Izmailian, Ralph Kenna, and Vladimir V. Papoyan, Exact coefficients of finite-size corrections in the Ising model with Brascamp-Kunz boundary conditions and their relationships for strip and cylindrical geometries, arXiv:2303.03484 [cond-mat.stat-mech], 2023. See also J. Phys. A: Math. Theor, (2023).
FORMULA
a(n) ~ (-1)^n * 2^(2*n+5/4)*n^(2*n) / (exp(2*n)*log(1+sqrt(2))^(2*n+1/2)). - Vaclav Kotesovec, Oct 30 2013
MATHEMATICA
Table[n!*SeriesCoefficient[ArcSinh[Sin[x]], {x, 0, n}], {n, 1, 40, 2}] (* Vaclav Kotesovec, Oct 30 2013 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Patrick Demichel (patrick.demichel(AT)hp.com)
STATUS
approved