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# Manual Reference Pages  -  MATH::SYMBOLIC::AUXFUNCTIONS (3)

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### NAME

Math::Symbolic::AuxFunctions - Auxiliary functions for Math::Symbolic hierarchy

### SYNOPSIS

```

use Math::Symbolic::AuxFunctions;

Math::Symbolic::AuxFunctions::acos(\$x);
# etc

```

### DESCRIPTION

This module contains implementations of some auxiliary functions that are used within the Math::Symbolic hierarchy of modules. In particular, this module holds all trigonometric functions used for numeric evaluation of trees by Math::Symbolic::Operator.

#### EXPORT

None. On purpose. If I wished this module would pollute others’ namespaces, I’d have put the functions right where they’re used.

### TRIGONOMETRIC FUNCTIONS

#### tan

Computes the tangent sin(x) / cos(x).

#### cot

Computes the cotangent cos(x) / sin(x).

#### asin

Computes the arc sine asin(z) = -i log(iz + sqrt(1-z*z)). Above formula is for complex numbers.

#### acos

Computes the arc cosine acos(z) = -i log(z + sqrt(z*z-1)). Above formula is for complex numbers.

#### atan

Computes the arc tangent atan(z) = i/2 log((i+z) / (i-z)). Above formula is for complex numbers.

#### acot

Computes the arc cotangent ( atan( 1 / x ) ).

#### asinh

Computes the arc hyperbolic sine asinh(z) = log(z + sqrt(z*z+1))

#### acosh

Computes the arc hyperbolic cosine acosh(z) = log(z + sqrt(z*z-1)).

### OTHER FUNCTIONS

#### binomial_coeff

Calculates the binomial coefficient n over k of its first two arguments (n, k).

Code taken from Orwant et al, Mastering Algorithms with Perl

#### bell_number

The Bell numbers are defined as follows:

```

B_0   = 1
B_n+1 = sum_k=0_to_n( B_k * binomial_coeff(n, k) )

```

This function uses memoization.

### AUTHOR

Please send feedback, bug reports, and support requests to the Math::Symbolic support mailing list: math-symbolic-support at lists dot sourceforge dot net. Please consider letting us know how you use Math::Symbolic. Thank you.

If you’re interested in helping with the development or extending the module’s functionality, please contact the developers’ mailing list: math-symbolic-develop at lists dot sourceforge dot net.

List of contributors:

```

Steffen MXller, symbolic-module at steffen-mueller dot net
Stray Toaster, mwk at users dot sourceforge dot net
Oliver EbenhXh

```