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bundles / scipy 1.17.1 / scipy / special / _basic / factorial2

function

scipy.special._basic:factorial2

source: /scipy/special/_basic.py :2996

Signature

def   factorial2 ( n ,  exact = False ,  extend = zero )

Summary

Double factorial.

Extended Summary

This is the factorial with every second value skipped. E.g., 7!! = 7 * 5 * 3 * 1. It can be approximated numerically as 

n!! = 2 ** (n / 2) * gamma(n / 2 + 1) * sqrt(2 / pi)  n odd
    = 2 ** (n / 2) * gamma(n / 2 + 1)                 n even
    = 2 ** (n / 2) * (n / 2)!                         n even

The formula for odd n is the basis for the complex extension.

Parameters

n : int or float or complex (or array_like thereof)

Input values for n!!. Non-integer values require extend='complex'. By default, the return value for n < 0 is 0.

exact : bool, optional

If exact is set to True, calculate the answer exactly using integer arithmetic, otherwise use above approximation (faster, but yields floats instead of integers). Default is False.

extend : string, optional

One of 'zero' or 'complex'; this determines how values n<0 are handled - by default they are 0, but it is possible to opt into the complex extension of the double factorial. This also enables passing complex values to n.

Returns

nf : int or float or complex or ndarray

Double factorial of n, as integer, float or complex (depending on exact and extend). Array inputs are returned as arrays.

Examples

from scipy.special import factorial2
factorial2(7, exact=False)
factorial2(7, exact=True)
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Aliases

  • scipy.special.factorial2