Hi,
I tested on SMC, SageMath 6.10.
Consider the numerical integral:
def T(v):
def f(t): return (tanh(exp(i*t))/exp(i*t*v)).real()
c = integral_numerical(f(t), 0, 2*pi)[0]
return (c*gamma(v+1)/(2*pi)).n()
print [round(T(n)) for n in range(10)]
Sage returned: [0, 1, 0, -1, 0, 8, 0, -136, 0, 3968]
I expected: [0, 1, 0, -2, 0, 16, 0, -272, 0, 7936]
Looks like there is a factor of 2 missing somewhere.
Checked with Maple:
T := proc(v) local f,c;
f := t -> Re(tanh(exp(I*t))/exp(I*t*v));
c := int(f(t), t=0..2*Pi);
round(evalf(c*GAMMA(v+1)/(2*Pi))) end:
seq(T(n), n=0..9);
Peter
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