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The Maxima on-line user's manual

Algebra Calculator

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Hypergeometric Calculator

Hypergeometric

Function: hypergeometric ([<a1>, ..., <ap>],[<b1>, ... ,<bq>], x) The hypergeometric function. Unlike Maximas %f hypergeometric function, the function hypergeometric is a simplifying function; also, hypergeometric supports complex double and big floating point evaluation. For the Gauss hypergeometric function, that is p = 2 and q = 1, floating point evaluation outside the unit circle is supported, but in general, it is not supported.

fpprec:300;
float(hypergeometric([1,1,1],[1],1));

When the option variable expand_hypergeometric is true (default is false) and one of the arguments a1 through ap is a negative integer (a polynomial case), hypergeometric returns an expanded polynomial.

     Examples:
           (%i1)  hypergeometric([],[],x);
           (%o1) %e^x
     Polynomial cases automatically expand when expand_hypergeometric
     is true:
           (%i2) hypergeometric([-3],[7],x);
           (%o2) hypergeometric([-3],[7],x)

           (%i3) hypergeometric([-3],[7],x), expand_hypergeometric : true;
           (%o3) -x^3/504+3*x^2/56-3*x/7+1
     Both double float and big float evaluation is supported:
           (%i4) hypergeometric([5.1],[7.1 + %i],0.42);
           (%o4) 1.346250786375334-0.0559061414208204*%i

           (%i5) hypergeometric([5,6],[8], 5.7 - %i);
           (%o5) 0.00737582400977495-0.00104981368857867*%i

           (%i6) hypergeometric([5,6],[8], 5.7b0 - %i), fpprec : 30;
           (%o6) 7.37582400977494674506442010824b-3-1.04981368857867315858055393376b-3*%i

There are also some inexact matches for hypergeometric. Try ?? hypergeometric to see them.

(%o1)                                true
(%i2) 

Hypergeometric Example

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