.98894455174110533610842263322837782131586088706273391078199240163901519469\ 80181964119104689997999337856216264172674995829423594452606969109906374\ 26028189043375839785170633107527839938730968351226479455609207435230051\ 7201616621624193448888017317445002269389 (256 digits), is the number. 4 - 1/768 Psi(3, 3/4) + 1/96 Pi also known as beta(4), or Sum((-1)*(n+1)/n^4,n=0..infinity). See Abramowitz and Stegun.