A144663 Decimal expansion of Product_{n>=2} (n^4-1)/(n^4+1).

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

Offset: 0

Author

R. J. Mathar, Feb 01 2009

Keywords

• nonn
• cons

Examples

			0.8480540493529003921296501834...
		

Links

• J. Borwein et al., Experimentation in Mathematics, 2004, section 1.2.
• László Tóth, Transcendental Infinite Products Associated with the ±1 Thue-Morse Sequence, Journal of Integer Sequences, Vol. 23 (2020), Article 20.8.2.
• Eric Weisstein's World of Mathematics, Infinite Product.

Crossrefs

Cf. A090986, A255434.

Programs

Maple

Digits := 120 :
m := 1:
for r from 2 to 10 do
omega := cos(Pi/r)+I*sin(Pi/r) :
x := (-1)^(m+1)*2*m*m!/r*mul( GAMMA(-m*omega^j)^(-(-1)^j),j=1..2*r-1) ;
x := Re(evalf(x)) ;
print(r,x) ;
od:

Mathematica

RealDigits[ -1/2*Pi*Csc[(-1)^(1/4)*Pi]*Csc[(-1)^(3/4)*Pi]*Sinh[Pi] // Re, 10, 105] // First (* Jean-François Alcover, Feb 11 2013 *)
RealDigits[Re[N[Product[(n^4 - 1)/(n^4 + 1), {n, 2, Infinity}], 110]]][[1]] (* Bruno Berselli, Apr 02 2013 *)

PARI

Pi*sinh(Pi)/(cosh(Pi*sqrt(2))-cos(Pi*sqrt(2))) \\ Michel Marcus, Sep 07 2020

Formula

Equals Pi*sinh(Pi) / (cosh(sqrt(2)*Pi) - cos(sqrt(2)*Pi)). - Vaclav Kotesovec, Dec 08 2015

Extensions

More terms from Jean-François Alcover, Feb 11 2013