A144669 Decimal expansion of Product_{n=2..infinity} (n^10-1)/(n^10+1).

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

Offset

0,1

Links

Table of n, a(n) for n=0..104.

J. Borwein et al., Experimentation in Mathematics, 2004, section 1.2.

E. W. Weisstein, Infinite Product, MathWorld.

Index entries for transcendental numbers.

Example

0.99801282617298278419003981450896856553...

Mathematica

f[k_] := Sin[(-1)^(k/10)*Pi]; RealDigits[Pi/(5*Sinh[Pi])*Product[f[k], {k, {2, 4, 6, 8}}]/ Product[f[k], {k, {1, 3, 7, 9}}] // Re, 10, 105] // First (* Jean-François Alcover, Feb 12 2013 *)

Prog

(PARI) prodnumrat(1-2/(n^10+1), 2) \\ Charles R Greathouse IV, Apr 29 2026
(PARI) real(vecprod(apply(y->gamma(2-y), polroots(x^10+1)))/vecprod(apply(y->gamma(2-y), polroots(x^10-1)))) \\ Charles R Greathouse IV, Apr 29 2026
(PARI) z(t)=exp(I*Pi*t)
Pi/(5*sinh(Pi)) * abs(sin(Pi*z(1/5))*sin(Pi*z(2/5)))^2 / abs(sin(Pi*z(1/10))*sin(Pi*z(3/10)))^2 \\ Charles R Greathouse IV, Apr 29 2026
(PARI) f(t)=sin(Pi*exp(I*Pi*t))^2
Pi/5*abs(f(.2)*f(.4)/f(.1)/f(.3))/sinh(Pi) \\ Charles R Greathouse IV, Apr 29 2026

Crossrefs

Cf. A090986.

Sequence in context: A244347 A388892 A341901 * A344688 A346451 A347059

Adjacent sequences: A144666 A144667 A144668 * A144670 A144671 A144672

Keyword

nonn,cons,easy

Author

R. J. Mathar, Feb 01 2009

Extensions

More terms from Jean-François Alcover, Feb 12 2013

Status

approved