how to calculate the gamma function when the variables are the complex numbers?

hello ,everyone! Now I need to calculate the two gamma functions in parabolic nondiffacting optical wavefields, and , where the variables are the complex numbers. In generally, we use the gamma function in MATLAB, which the variables are the real number. so could do please tell me how to calculate the values? Thank you very much!

For more information about gamma function :

"Parabolic nondiffracting optical wavefields,"

Miguel A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda

Optics Letters, 29(1), 44-46 (2004) ( http://goo.gl/KhmqQY )

Answer 1

[Walter Roberson]

The Symbolic Toolbox can calculate it.

format long g
a = sym(complex(randn, randn))

a = 

g1 = gamma(1/4 + 1/2*1i*a)

g1 = 

double(g1)

ans = 
          0.168376614679118 +     0.549688232146916i

[Zhang Yong]

thank you very much for your answer !