AlternatingFactorial

AlternatingFactorial[n]

gives the alternating factorial .

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The satisfies the recurrence relation with .
  • AlternatingFactorial can be evaluated to arbitrary numerical precision.
  • AlternatingFactorial automatically threads over lists.

Examples

open all close all

Basic Examples  (4)

Compute the first several alternating factorial numbers:

In[1]:=
Click for copyable input
Out[1]=

Plot the values on a log scale:

In[2]:=
Click for copyable input
Out[2]=

Expand the alternating factorial in terms of other functions:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=

Give the closed form of the following alternating sum:

In[1]:=
Click for copyable input
Out[1]=

The alternating factorial numbers give the solution to the following recurrence:

In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=

Scope  (11)

Introduced in 2014
(10.0)