# 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.
• AlternatingFactorial can be used with Interval and CenteredInterval objects. »

# 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(17)

### Numerical Evaluation(4)

Evaluate numerically:

Evaluate to high precision:

Evaluate efficiently at high precision:

AlternatingFactorial can be used with Interval and CenteredInterval objects:

### 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(8)

Real domain of AlternatingFactorial:

Complex domain:

Show a typeset form:

AlternatingFactorial is not an analytic function:

AlternatingFactorial has both singularity and discontinuity for z-2:

AlternatingFactorial is neither nondecreasing nor nonincreasing:

AlternatingFactorial is not injective:

AlternatingFactorial is neither non-negative nor non-positive:

It is non-negative on the non-negative reals:

AlternatingFactorial is neither convex nor concave:

## Applications(1)

As a definition, the following sum is AlternatingFactorial:

Check it numerically: