# AlternatingFactorial

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

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## Basic Examples(6)

Compute the first several alternating factorial numbers:

Plot the values on a log scale over a subset of the reals:

Plot over a subset of the complexes:

Expand the alternating factorial in terms of other functions:

Give the closed form of the following alternating sum:

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

## Scope(11)

### Numerical Evaluation(3)

Evaluate numerically:

Evaluate to high precision:

Evaluate efficiently at high precision:

### Specific Values(3)

Values of AlternatingFactorial at fixed points:

Value at zero:

Evaluate symbolically:

### Visualization(2)

Plot the absolute value of AlternatingFactorial:

Plot the real part of :

Plot the imaginary part of :

### Function Properties(3)

Real domain of AlternatingFactorial:

Complex domain: