% Written by Min-Hua Huang
% June 9, 2011
% Figure 2 of "Indefinite Integration of the Gamma Integral".
% Functional Plots of ${\exp(-x)}$ and $h_{s}^{x}$ when s is a non-integer.
clear; clc; format long;
record=ones(61,8)*-999; record(:,1)=-4:0.1:2;
record(:,2)=exp(-record(:,1)); kk=3; n2=10^5;
%***************************** h(0:2,c,0) *******************************
for i=0.5:-1:-4.5
    kkk=1;
    for c=-4:0.1:2
        record(kkk,kk)=h(i,c,n2); 
        kkk=kkk+1;
    end
    kk=kk+1;
end   
x=record(:,1);
y1=record(:,2);
y2=record(:,3);
y3=record(:,4);
y4=record(:,5);
y5=record(:,6);
y6=record(:,7);
y7=record(:,8);
plot(x,y1,'-k','LineWidth',2)
hold on
plot(x,y2,'-k+','MarkerSize',4)
plot(x,y3,':k','LineWidth',2)
plot(x,y4,'-.k','LineWidth',2)
plot(x,y5,'-ks','MarkerSize',4)
plot(x,y6,'-k^','MarkerSize',4)
plot(x,y7,'--k','LineWidth',2)
hold off
axis([-4, 2, -20, 20]);
box off;
xlabel('x');
ylabel('values of exp(-x) and h(s,x)')
legend('exp(-x)','h(0.5,x)','h(-0.5,x)','h(-1.5,x)','h(-2.5,x)','h(-3.5,x)','h(-4.5,x)');