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<A NAME=Special_Function_Package>

<TITLE>Special_Function_Package</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>SPECIAL FUNCTION PACKAGE</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>introduction</B>
<P>
<P>
 
The REDUCE <em>Special Function Package</em> supplies extended 
algebraic and numeric support for a wide class of objects. 
This package was released together with REDUCE 3.5 (October 1993) 
for the first time, a major update is released with REDUCE 3.6. 
<P>
<P>
The functions included in this package are in most cases (unless otherwise 
stated) defined and named like in the book by Abramowitz and Stegun: 
Handbook of Mathematical Functions, Dover Publications. 
<P>
<P>
The aim is to collect as much information on the special functions 
and simplification capabilities as possible, 
i.e. algebraic simplifications and numeric (rounded mode) code, limits 
of the functions together 
with the definitions of the functions, which are in most cases a power 
series, a (definite) integral and/or a differential equation. 
<P>
<P>
What can be found: Some famous constants, a variety of Bessel functions, 
special polynomials, 
the Gamma function, the (Riemann) Zeta function, Elliptic Functions, Elliptic 
Integrals, 3J symbols (Clebsch-Gordan coefficients) and integral functions. 
<P>
<P>
What is missing: Mathieu functions, LerchPhi, etc.. 
The information about the special functions which solve certain 
differential equation is very limited. 
In several cases numerical approximation is restricted to real 
arguments or is missing completely. 
<P>
<P>
The implementation of this package uses REDUCE rule sets to a large extent, 
which guarantees a high 'readability' of the functions definitions in the 
source file directory. It makes extensions to the special 
functions code easy in most cases too. To look at these rules 
it may be convenient to use the showrules operator e.g. 
<P>
<P>

<A HREF=r37_0178.html>showrules</A>Besseli; 
<P>
<P>
. 
<P>
<P>
Some evaluations are improved if the special function package is loaded, 
e.g. some (infinite) sums and products leading to expressions including 
special functions are known in this case. 
<P>
<P>
Note: The special function package has to be loaded explicitly by calling 
<P><PRE><TT>
   load_package specfn;
</TT></PRE><P><P>
<P>
The functions 
<A HREF=r37_0529.html>MeijerG</A> and 
<A HREF=r37_0528.html>hypergeometric</A> require 
additionally 
<P><PRE><TT>
   load_package specfn2;
</TT></PRE><P><P>
<P>