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

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       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 M�ller, symbolic-module at steffen-mueller dot net
         Stray Toaster, mwk at users dot sourceforge dot net
         Oliver Ebenh�h

       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.

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

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.

       New versions of this module can be found on http://steffen-mueller.net or CPAN. The module development
       takes place on Sourceforge at http://sourceforge.net/projects/math-symbolic/

       Math::Symbolic

perl v5.40.0                                       2024-09-16                  Math::Symbolic::AuxFunctions(3pm)

         use Math::Symbolic::AuxFunctions;

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

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)).