[SciPy-User] docs: properties of special functions
josef.pktd@gmai...
josef.pktd@gmai...
Tue Sep 4 13:41:07 CDT 2012
The scipy.special special function docstrings are very skinny.
What's a good source to quickly find some properties of the special functions?
---
For example, the distributions make heavy use of the special
functions, but I'm finding derivatives only by accident:
What's the derivative of i0? answer ask mpmath documentation
>>> mp.besseli(0, 1, derivative=0)
mpf('1.2660658777520084')
>>> mp.besseli(0, 1, derivative=1)
mpf('0.56515910399248503')
>>> special.i0(1)
1.2660658777520082
>>> special.i1(1)
0.56515910399248515
What's the derivative of gamma and loggamma? ask sympy
>>> import sympy as sy
>>> sy.diff(sy.gamma(a), a)
gamma(a)*polygamma(0, a)
>>> sy.diff(sy.loggamma(a), a) #unknown derivative ?
D(loggamma(a), a)
>>> import statsmodels.tools.numdiff as nd
>>> nd.approx_fprime_cs(np.array([5.]), special.gammaln).item()
1.5061176684318003
>>> special.polygamma(0,5)
array(1.5061176684318003)
but going through the list in scipy.special, I actually find
"derivative of the logarithm of the gamma function"
>>> special.psi(5)
1.5061176684318003
Josef
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