A258412 Decimal expansion of Integral_{x=0..1} Product_{k>=1} (1-x^k)^k dx.

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

Offset: 0

Author

Vaclav Kotesovec, May 29 2015

Keywords

• nonn
• cons

Comments

Integral_{x=0..1} Product_{k=1..n} (1+x^k)^k dx ~ 3*2^(n*(n+1)/2 + 1)/n^3.

Integral_{x=0..1} Product_{k=1..n} (1+x^k) dx ~ 2^(n+2)/n^2.

Integral_{x=0..1} Product_{k>=1} (1-x^k) dx = A258232 = 0.3684125359314...

Integral_{x=0..1} Product_{k=1..n} (1-x^k)^n dx ~ 1/n.

Integral_{x=0..1} Product_{k=1..n} (1+x^k)^n dx ~ 2^(n^2 + 2)/n^3.

Examples

			0.298783365106567298770953772114...
		

Links

• Vaclav Kotesovec, The integration of q-series

Crossrefs

Cf. A073592, A258232.

Extensions

More digits from Vaclav Kotesovec, Oct 10 2023