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hankel_1

hankel_1(2/3,0.5);

Calculate

hankel_1

hankel_1(2/3,0.5);

hankel_1(2/5,0.5);

Calculate

hankel_1

hankel_1(1,0.5);

Calculate

hankel_1

hankel_1(2/3,0.5);

Calculate

hankel_1

hankel_1(2/3,0.5);

hankel_1(2/5,0.5);

Calculate

hankel_1

hankel_1(1,0.5);

Calculate

hankel_1

Run Example
(%i1)hankel_1(1,0.5);
(%o1)               0.24226845767487 - 1.471472392670243 %i
(%i2) 
Run Example
fn(x,N) := sin(x) + sum((-1)^i*cos(x),i,0,N);
                                             i
(%o1)          fn(x, N) := sin(x) + sum((- 1)  cos(x), i, 0, N)
(%i2) plot2d(fn(x,10),[x,0,%pi *2]);
plotplot2d(fn(x,10),[x,0,%pi *2]);kso(ka,N) := 4 * abs(bessel_j(0,ka)/hankel_1(0,ka) + 2*sum( ((-1)^n*bessel_j(n,ka)/hankel_1(n,ka)),n,1,N))^2;
(%o3) kso(ka, N) := 4
                                                                              2
                    !                             n                          !
                    !bessel_j(0, ka)         (- 1)  bessel_j(n, ka)          !
                    !--------------- + 2 sum(----------------------, n, 1, N)!
                    !hankel_1(0, ka)            hankel_1(n, ka)              !
(%i4) 
Run Example
kso(ka,N) := 4 * abs(bessel_j(0,ka)/abs(hankel_1(0,ka)) + 2*sum( ((-1)^n*bessel_j(n,ka)/abs(hankel_1(n,ka))),n,1,N))^2;
(%o1) kso(ka, N) := 4
                                                                              2
               !                                  n                          !
               !  bessel_j(0, ka)            (- 1)  bessel_j(n, ka)          !
               !-------------------- + 2 sum(----------------------, n, 1, N)!
               !abs(hankel_1(0, ka))          abs(hankel_1(n, ka))           !
(%i2) plot2d(kso(ka,14), [ka,0.0,8.0]);
plotplot2d(kso(ka,14), [ka,0.0,8.0]);

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