mu = -0.1;
beta = -0.5;
sigma = 2.5;
a = 90;
b = 120;
m = -1/(4*beta); m1 = m - 1/2;
a1 = mu/(sigmasigmabeta)a^(-2beta);
b1 = mu/(sigmasigmabeta)b^(-2beta);
MyF[k_] := Gamma[ m - k](WhittakerW[k, m1, b1]WhittakerM[k, m1, a1] - WhittakerM[k, m1, b1]*WhittakerW[k, m1, a1]);
this code MyF[1000]=0.
But for this code:
MyF1[k_] := N[ Gamma[Rationalize[ m - k]](WhittakerM[Rationalize[k], 0, Rationalize[a1]] WhittakerW[Rationalize[k], 0, Rationalize[b1]] - WhittakerM[Rationalize[k], 0, Rationalize[b1]] WhittakerW[ Rationalize[k], 0, Rationalize[a1]]), 5];
MyF1[1000]=0.044810;