Evaluation of ζ(2) by the definition (sort of) [HP-42S & HP-71B]

[Albert Chan]

If we add a 1 CF correction term to initial b, result is even better.

LET b = SQR(5)
LET b = (4*(b-2)*x2+0.8*x+0.12*b - 3.2/(50*x+23*b))/(10-c)

n = 100
Accurate digits = 223.10474793591716
n = 101
Accurate digits = 225.21595297592808
n = 102
Accurate digits = 227.3269505519926
n = 400
Accurate digits = 853.05677365480504
n = 401
Accurate digits = 855.15205424416744
n = 402
Accurate digits = 857.24732141737914

For n=471, it reached 1000 digits full precision.