Status: New
Owner: ----
Labels: Type-Defect Priority-Medium
New issue 4125 by [email protected]: Issues with Bessel functions
http://code.google.com/p/sympy/issues/detail?id=4125
I am using version 0.7.2 and have identified three problems involving the
Bessel functions. These were found in association with trying to solve the
ODE -y"/2+y/x=0
-----------------------------------------------------------------------
1) sympy appears to be unable to solve this ODE.
from sympy import *
x = Symbol('x')
y = Function('y')
dsolve(-Derivative(y(x),x,x)/2+y(x)/x,y(x))
Traceback (most recent call last):
File "<input>", line 1, in <module>
File "/usr/lib/python2.7/dist-packages/sympy/solvers/ode.py", line 528,
in dsolve
raise NotImplementedError("dsolve: Cannot solve " + str(eq))
NotImplementedError: dsolve: Cannot solve -Derivative(y(x), x, x)/2 + y(x)/x
Mathematica gives the two solutions, which I will denote as y1,y2 as
y1 = sqrt[x] BesselI[1,sqrt[8x]]
y2 = sqrt[x] BesselK[1,sqrt[8x]]
----------------------------------------------------------------------
2) sympy seems to have a problem with taking the following limit
limit(x*diff(y1,x,x)/y1,x,0) # This should equal 2 for any x>=0
sympy returns -oo (same for y2)
You do get the right answer using
limit(x*diff(a1,x,x)/a1,x,1).evalf() # this returns 2
limit(x*diff(a1,x,x)/a1,x,1e-16).evalf() # this is off by about 5%
3) lambdify has trouble with Bessel functions when running a script.
The following code works fine in bpython
import sympy as sy
import numpy as np
if __name__ == '__main__':
x = sy.Symbol('x')
y = sy.exp(x)
z = sy.besselj(1,x)
print(y)
print(z)
Y = sy.lambdify(x,y,'numpy')
print(Y(0))
Z = sy.lambdify(x,z,'numpy')
print(Z(0))
However, if I save the script (attached) and run it the output is
exp(x)
besselj(1, x)
1.0
Traceback (most recent call last):
File "lambidfy_bessel.py", line 18, in <module>
print(Z(0))
File "<string>", line 1, in <lambda>
NameError: global name 'besselj' is not defined
Attachments:
lambidfy_bessel.py 260 bytes
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