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The Maxima on-line user's manual

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Bessel_j

Function: bessel_j (<v>, <z>) The Bessel function of the first kind of order v and argument z.

plot2d(bessel_j(0,x),[x,-3,3]);

bessel_j is defined as

inf ==== k - v - 2 k v + 2 k \ (- 1) 2 z > -------------------------- / k! gamma(v + k + 1) ==== k = 0

although the infinite series is not used for computations.

There are also some inexact matches for bessel_j. Try ?? bessel_j to see them.

(%o1)                                true
(%i2) 

Related Examples

bessel_j-true

bessel_reduce:true;

bessel_j(2,x);

bessel_j(4,2);

Calculate

bessel_j-bessel_y-plot2d
plot2d(bessel_j(0,x)*bessel_y(1,0.8)/(bessel_j(0,1)*bessel_y(1,0.8)-bessel_y(0,1)*bessel_j(1,0.8))-bessel_y(0,x)*bessel_j(1,0.8)/(bessel_j(0,1)*bessel_y(1,0.8)-bessel_y(0,1)*bessel_j(1,0.8))-1,[x,0,200]);

plot2d(bessel_j(0,x)*...

Calculate

bessel_j-integrate-sqrt

integrate(bessel_j(1,...

Calculate

bessel_j-plot2d-sqrt
plot2d(bessel_j(1,sqrt(t^2-1)*100)*100/sqrt(t^2-1),[t,1,2]);

plot2d(bessel_j(1,sqr...

Calculate

bessel_j-exp-expintegral_e1-first-inf-quad_qagi

h=1.79804/8*exp(0.013...

f(x):= exp(-x^...

z(r):=1.79804/4*(f...

Calculate

bessel_j-exp-expintegral_e1-first-inf-quad_qagi

h=1/8*exp(0.01150959/...

f(x):= exp(-x^...

z(r):=1/4*(first(q...

Calculate

bessel_j-exp-expintegral_e1-first-inf-quad_qagi

h=1/8*exp(0.0125)*(ex...

f(x):= exp(-x^2/8)/(0...

z(r):=1/4*(first(quad...

Calculate

bessel_j-exp-expand-imagpart-plot3d-realpart
plot3d(ber(n,x),[n,-5,5],[x,-5,5]);

ber(n,x):= realpart(e...

bei(n,x):= imagpart(e...

plot3d(ber(n,x),[n,-5...

Calculate

bessel_j-exp-expintegral_e1-first-inf-quad_qagi

h=1/8*exp(8.965753/8)...

f(x):= exp(-x^2...

z(r):=1/4*(first(q...

Calculate

bessel_j-exp-expintegral_e1-first-inf-quad_qagi

h=1/8*exp(0.0125)*(ex...

f(x):= exp(-x^2...

z(r):=1/4*(first(q...

Calculate