A354296 Decimal expansion of Product_{k>=1} (1 - exp(-2*k*Pi/sqrt(3))).

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

Offset

0,1

Comments

Note that Prudnikov incorrectly give this product as 3^(1/4)*exp(-Pi*sqrt(3)/18), which differs from the correct result by 0.0000182...

References

A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 1 (Overseas Publishers Association, Amsterdam, 1986), p. 757, section 6.2.3, incorrect formula 4.

Links

Table of n, a(n) for n=0..105.

Eric Weisstein's World of Mathematics, Infinite Product, formula 52.

Example

0.972713586936242371513055024334538082849547588619101318683993472802594...

Maple

evalf(Product(1 - exp(-2*k*Pi/sqrt(3)), k = 1..infinity), 105);

Mathematica

RealDigits[QPochhammer[E^(-2*Pi/Sqrt[3])], 10, 105][[1]]

Prog

(PARI) prodinf(k=1, (1 - exp(-2*k*Pi/sqrt(3))))

Crossrefs

Cf. A292828.

Sequence in context: A029688 A155792 A381156 * A247226 A197834 A173515

Adjacent sequences: A354293 A354294 A354295 * A354297 A354298 A354299

Keyword

nonn,cons

Author

Vaclav Kotesovec, May 23 2022

Status

approved