A292828 - OEIS

A292828

Decimal expansion of Product_{k>=1} (1 + exp(-Pi*(2*k-1))).

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

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OFFSET

1,3

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, formula 5.

LINKS

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Infinite Product, formula 50.

Index entries for transcendental numbers.

FORMULA

Equals 2^(1/4) * exp(-Pi/24).

Equals A292820 / A292821.

Conjecture: Equals Sum_{k>=0} A000700(k) / exp(k*Pi). - Simon Plouffe, Sep 09 2025

EXAMPLE

1.043298262644687012527875688815591456103311209998752645741477289470472...

MATHEMATICA

RealDigits[2^(1/4) * E^(-Pi/24), 10, 120][[1]]