scipy.special.itj0y0#

scipy.special.itj0y0(x,out=None)=<ufunc'itj0y0'>#

Integrals of Bessel functions of the first kind of order 0.

Computes the integrals

\[\begin{split}\int_0^x J_0(t) dt \\\int_0^x Y_0(t) dt.\end{split}\]

For more on\(J_0\) and\(Y_0\) seej0 andy0.

Parameters:

xarray_like

Values at which to evaluate the integrals.

outtuple of ndarrays, optional

Optional output arrays for the function results.

Returns:

ij0scalar or ndarray

The integral ofj0

iy0scalar or ndarray

The integral ofy0

References

[1]

S. Zhang and J.M. Jin, “Computation of Special Functions”,Wiley 1996

Examples

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Evaluate the functions at one point.

>>>fromscipy.specialimportitj0y0>>>int_j,int_y=itj0y0(1.)>>>int_j,int_y(0.9197304100897596, -0.637069376607422)

Evaluate the functions at several points.

>>>importnumpyasnp>>>points=np.array([0.,1.5,3.])>>>int_j,int_y=itj0y0(points)>>>int_j,int_y(array([0.        , 1.24144951, 1.38756725]), array([ 0.        , -0.51175903,  0.19765826]))

Plot the functions from 0 to 10.

>>>importmatplotlib.pyplotasplt>>>fig,ax=plt.subplots()>>>x=np.linspace(0.,10.,1000)>>>int_j,int_y=itj0y0(x)>>>ax.plot(x,int_j,label=r"$\int_0^x J_0(t)\,dt$")>>>ax.plot(x,int_y,label=r"$\int_0^x Y_0(t)\,dt$")>>>ax.legend()>>>plt.show()

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