0,2

arcsin(x) is usually written as x + x^3/(2*3) + 1*3*x^5/(2*4*5) + 1*3*5*x^7/(2*4*6*7) + ..., = x + 1/6*x^3 + 3/40*x^5 + 5/112*x^7 + 35/1152*x^9 + 63/2816*x^11 + ... when reduced to lowest terms.

arccos(x) = Pi/2 - (x + 1/6*x^3 + 3/40*x^5 + 5/112*x^7 + 35/1152*x^9 + 63/2816*x^11 + ...).

arccsc(x) = 1/x+1/(6*x^3)+3/(40*x^5)+5/(112*x^7)+35/(1152*x^9)+63/(2816*x^11)+...

arcsec(x) = Pi/2 -(1/x+1/(6*x^3)+3/(40*x^5)+5/(112*x^7)+35/(1152*x^9)+63/(2816*x^11)+...)

arcsinh(x) = x-1/6*x^3+3/40*x^5-5/112*x^7+35/1152*x^9-63/2816*x^11+...

arccsc(x) = arcsin(1/x) and arcsec(x) = arccos(1/x): 1 < |x|

arcsch(x) = arsinh(1/x) for 1 < |x|

Also denominator of (2n-1)!! / (2n+1)*(2n)!! (n>0).

W. G. Bickley and J. C. P. Miller, Numerical differentiation near the limits of a difference table, Phil. Mag., 33 (1942), 1-12 (plus tables).

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 88.

H. B. Dwight, Tables of Integrals and Other Mathematical Data, Macmillan, NY, 1968, Chap. 3.

Focus, vol. 16, no. 5, page 32, Oct 1996.

H. E. Salzer, Coefficients for expressing the first twenty-four powers in terms of the Legendre polynomials, Math. Comp., 3 (1948), 16-18.

T. D. Noe, Table of n, a(n) for n=0..200

Eric Weisstein's World of Mathematics, Inverse Cosecant

Eric Weisstein's World of Mathematics, Inverse Cosine

Eric Weisstein's World of Mathematics, Inverse Secant

Eric Weisstein's World of Mathematics, Inverse Sine

Eric Weisstein's World of Mathematics, Inverse Hyperbolic Cosecant

Eric Weisstein's World of Mathematics, Inverse Hyperbolic Sine

Eric Weisstein's World of Mathematics, Archimedes' Spiral

A055786(n) / a(n) = A001147(n) / ( A000165(n) * (2*n+1))

Sequence in context: A045565 A110424 A114079 this_sequence A089207 A027777 A073773

Adjacent sequences: A002592 A002593 A002594 this_sequence A002596 A002597 A002598

nonn,frac,nice,easy

njas