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I want to calculate the integral or derivative of the modified Bessel functions in python. I want to calculate the infinite integral (without limits). Recently I found a method to do this. You can see an example for a simple function (x**2) below:

from sympy import *
x = Symbol('x')
print integrate(x**2, x)

The result is: x^3/3 . But when I put a modified Bessel function instead of x**2:

import scipy.integrate as integrate
import scipy.special as special
from scipy import integrate
from sympy import *

x = Symbol('x')
print integrate(special.iv(1,x), x)

In this case I get this error:

AttributeError: 'module' object has no attribute 'iv'

It should be noted that the integral of Bessel function of the first kind is Bessel function of the zero kind. I expect to get: iv(0,x)

How can I do that in python?

Chris Martin
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Jafar
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  • mpmath does Bessel functions http://mpmath.org/doc/current/functions/bessel.html#bessel-functions-and-related-functions – PM 2Ring Jan 15 '17 at 06:05
  • You have to specify the complete module name: `integrate(scipy.special.iv(1,x), x)`. Unfortunately, despite the promise, apparently this function cannot be integrated by `numpy`. – DYZ Jan 15 '17 at 06:07

1 Answers1

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It can be easily integrated numerically, say from limit 1 to 10

from scipy import integrate
import scipy.special as sp
def f(x):
    return sp.iv(1,x)
I,err=integrate.quad(f,1,10)
print(I,err)

The result of Integral is 2814.4505625885026, Error is 3.124667816254981e-11

celerion
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