A195699 Decimal expansion of arcsin(sqrt(1/8)) and of arccos(sqrt(7/8)).

3, 6, 1, 3, 6, 7, 1, 2, 3, 9, 0, 6, 7, 0, 7, 8, 0, 5, 5, 8, 9, 1, 8, 8, 6, 7, 6, 3, 2, 0, 6, 6, 6, 6, 8, 1, 0, 1, 2, 6, 0, 9, 2, 4, 3, 2, 1, 2, 2, 2, 0, 1, 3, 3, 8, 1, 3, 3, 7, 7, 0, 6, 6, 2, 9, 1, 8, 5, 3, 6, 9, 0, 9, 5, 7, 3, 1, 5, 1, 3, 2, 4, 8, 2, 4, 1, 3, 8, 0, 5, 4, 6, 9, 5, 5, 0, 6, 5, 1, 8

Offset: 0

Author

Clark Kimberling, Sep 23 2011

Keywords

• nonn
• cons

Examples

			arcsin(sqrt(1/8)) = 0.3613671239067078055891886763206666...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for transcendental numbers

Crossrefs

Cf. A195700, A195703, A195704.

Programs

Magma

[Arcsin(Sqrt(1/8))]; // G. C. Greubel, Nov 18 2017

Mathematica

r = Sqrt[1/8];
N[ArcSin[r], 100]
RealDigits[%]  (* A195699 *)
N[ArcCos[r], 100]
RealDigits[%]  (* A168229 *)
N[ArcTan[r], 100]
RealDigits[%]  (* A188615 *)
N[ArcCos[-r], 100]
RealDigits[%]  (* A195704 *)

PARI

asin(sqrt(1/8)) \\ G. C. Greubel, Nov 18 2017

Formula

From Peter Bala, Jan 14 2022: (Start)

Equals (1/2)*arccos(3/4) = arctan(sqrt(7)/7).

Equals sqrt(7)*Sum_{n >= 0} 1/((16*n + 8)*(2^n)*binomial(2*n,n)).

Equals sqrt(2)*Sum_{n >= 0} binomial(2*n,n)/((8*n + 4)*32^n). (End)