OFFSET
0,1
COMMENTS
Also, decimal expansion of Integral_{x=0..1} (2 - (1-i)*x^(1-i) - (1+i)*x^(1+i))/(4 - 4*x) dx, where i is the imaginary unit.
FORMULA
Equals (1 - i)*(H(1-i) + i*H(1+i))/4, where H(z) is a harmonic number with complex argument.
Equals (Psi(i-1)-Psi(1)-i+1)/2-Pi*(i+1)*coth(Pi)/4), where Psi(x) is the digamma function. - Peter Luschny, Jan 27 2016
EXAMPLE
.297595969027714331872169889027156331536383020649824278231847237306809...
MAPLE
((1-I)*(harmonic(1-I) + I*harmonic(1+I)))/4:
Re(evalf(%, 106)); # Peter Luschny, Jan 27 2016
MATHEMATICA
(1 - I)*(HarmonicNumber[1 - I] + I*HarmonicNumber[1 + I])/4 // Re // RealDigits[#, 10, 100]& // First (* Jean-François Alcover, Jan 26 2016 *)
PROG
(Sage)
# Warning: Floating point calculation. Adjust precision as needed
# and use some guard digits!
from mpmath import mp, chop, psi, coth, pi
mp.dps = 108; mp.pretty = True
chop((psi(0, I-1)-psi(0, 1)-I+1)/2-pi*(I+1)*coth(pi)/4) # Peter Luschny, Jan 27 2016
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Bruno Berselli, Jan 26 2016
STATUS
approved