A390401 Decimal expansion of the real solution of sqrt(Pi)*erf(sqrt(-log(h))) - 2*h*sqrt(-log(h)) = sqrt(Pi)/2.

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

Offset

0,1

Comments

This constant gives the value of h such that the area between the graph of y = exp(-x^2) and the straight line y = h is equal to half of that between y = exp(-x^2) and the x-axis.

Links

Table of n, a(n) for n=0..99.

Example

0.30636228415302713291864810214053595344411492...

Mathematica

digits=100; RealDigits[h/.NSolve[Sqrt[Pi]Erf[Sqrt[-Log[h]]]-2h*Sqrt[-Log[h]]==Sqrt[Pi]/2, {h}, Reals, digits], 10, digits][[1]][[1]]

Crossrefs

Cf. A002161, A019704, A086751, A391400.

Sequence in context: A160770 A212225 A278085 * A356195 A051021 A294777

Adjacent sequences: A390398 A390399 A390400 * A390402 A390403 A390404

Keyword

nonn,cons

Author

Stefano Spezia, Dec 11 2025

Status

approved