"Fossies" - the Fresh Open Source Software Archive  

Source code changes of the file "mpmath/calculus/differentiation.py" between
mpmath-0.19.tar.gz and mpmath-1.0.0.tar.gz

About: mpmath is a Python library for arbitrary-precision floating-point arithmetic.

differentiation.py  (mpmath-0.19):differentiation.py  (mpmath-1.0.0)
skipping to change at line 455 skipping to change at line 455
i += 1 i += 1
@defun @defun
def differint(ctx, f, x, n=1, x0=0): def differint(ctx, f, x, n=1, x0=0):
r""" r"""
Calculates the Riemann-Liouville differintegral, or fractional Calculates the Riemann-Liouville differintegral, or fractional
derivative, defined by derivative, defined by
.. math :: .. math ::
\,_{x_0}{\mathbb{D}}^n_xf(x) \frac{1}{\Gamma(m-n)} \frac{d^m}{dx^m} \,_{x_0}{\mathbb{D}}^n_xf(x) = \frac{1}{\Gamma(m-n)} \frac{d^m}{dx^m}
\int_{x_0}^{x}(x-t)^{m-n-1}f(t)dt \int_{x_0}^{x}(x-t)^{m-n-1}f(t)dt
where `f` is a given (presumably well-behaved) function, where `f` is a given (presumably well-behaved) function,
`x` is the evaluation point, `n` is the order, and `x_0` is `x` is the evaluation point, `n` is the order, and `x_0` is
the reference point of integration (`m` is an arbitrary the reference point of integration (`m` is an arbitrary
parameter selected automatically). parameter selected automatically).
With `n = 1`, this is just the standard derivative `f'(x)`; with `n = 2`, With `n = 1`, this is just the standard derivative `f'(x)`; with `n = 2`,
the second derivative `f''(x)`, etc. With `n = -1`, it gives the second derivative `f''(x)`, etc. With `n = -1`, it gives
`\int_{x_0}^x f(t) dt`, with `n = -2` `\int_{x_0}^x f(t) dt`, with `n = -2`
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