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+//practical interpolation

+//example 3.10

+//page 97

+clc;clear;close;

+x=[0.61 0.62 0.63 0.64 0.65 0.66 0.67];

+y=[1.840431 1.858928 1.877610 1.896481 1.915541 1.934792 1.954237];

+h=0.01//interval between values of x

+c=1;

+for i=1:6

+    d1(c)=y(i+1)-y(i);

+    c=c+1;

+end

+c=1;

+for i=1:5

+    d2(c)=d1(i+1)-d1(i);

+    c=c+1

+end

+c=1;

+for i=1:4

+    d3(c)=d2(i+1)-d2(i);

+    c=c+1;

+end

+c=1;

+for i=1:3

+    d4(c)=d3(i+1)-d3(i);

+    c=c+1;

+end

+d=[d1(1) d2(1) d3(1) d4(1)];

+x0=0.644;

+p=(x0-x(4))/h;

+y_x=y(4);

+y_x=y_x+p*(d1(3)+d1(4))/2+p^2*(d2(2))/2;//stirling formula

+printf(' the value at %f by stirling formula is : %f\n\n',x0,y_x);

+y_x=y(4);

+y_x=y_x+p*d1(4)+p*(p-1)*(d2(3)+d2(4))/2;

+printf(' the value at %f by bessels formula is : %f\n\n',x0,y_x);

+y_x=y(4);

+q=1-p;

+y_x=q*y(4)+q*(q^2-1)*d2(3)/2+p*y(5)+p*(q^2-1)*d2(4)/2;

+printf(' the value at %f by everrets formula is : %f\n\n',x0,y_x);