### The Maxima on-line user's manual

Algebra 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.

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) ```

### Related Examples

##### hypergeometric

hypergeometric([],[],x);

Calculate

##### hypergeometric

hypergeometric([k,k-n...

Calculate

##### hypergeometric-makegamma-pochhammer-taylor

taylor(hypergeometric...

makegamma(pochhammer(...

Calculate

##### hypergeometric

? ?? hypergeometric;

Calculate

##### hypergeometric

hypergeometric([-0.5,...

Calculate

##### hypergeometric

? cdf_hypergeometric;

Calculate

##### hypergeometric-true

hypergeometric([a,a],...

Calculate

##### hypergeometric-makelist-sum-true

hypergeometric([],[],...

hypergeometric([1],[1...

hypergeometric([-1],[...

Calculate

##### hypergeometric-true

hypergeometric([],[],...

hypergeometric([1],[1...

hypergeometric([-1],[...

Calculate

##### hypergeometric-true

hypergeometric([],[],x);

hypergeometric([-3],...

hypergeometric([-3],...

Calculate