differentiation.py (mpmath-0.19) | : | differentiation.py (mpmath-1.0.0) | ||
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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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