References
21
angle in radians, and “conj” for the complex conjugate value. Each of the methods
can be applied either on the function values (value, default) or on the input variables
z (inz), a (ina), or b (inb).
Example
%% Data
x = linspace(-5,5,50);
% complex array
[X,Y] = meshgrid(x,x);
z = X+i * Y;
a = 0.75 - i * 0.25;
% randn+i * randn;
b = -0.5;
% randn;
obj = incbetaC(z,a,b);
% incomplete Beta function
%% Visualization
figure,surf(X,Y,obj.abs)
xlabel(’real(z)’),ylabel(’imag(z)’),zlabel(’abs’)
shg
figure,surf(X,Y,obj.real)
xlabel(’real(z)’),ylabel(’imag(z)’),zlabel(’real’)
shg
figure,surf(X,Y,obj.imag)
xlabel(’real(z)’),ylabel(’imag(z)’),zlabel(’imag’)
shg
References
1. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover Pub., New York
(1972)
2. Godfrey, P.: A note on the computation of the convergent Lanczos complex Gamma approximation (2015). http://my.fit.edu/~gabdo/gamma.txt
3. Gradstein, I.S., Rhysik, I.M.: Tafeln · Tables II. Verlag Harry Deutsch Thun, Frankfurt (1981)
4. Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes in Fortran 77.
Cambridge University Press, Cambridge (1986)
5. Pugh, G.R.: An Analysis of the Lanczos Gamma Approximation. Thesis, The University of
British Columbia (2004)