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<a name="Factorials"></a>
Next: <a rel="next" accesskey="n" href="Pochhammer-Symbol.html">Pochhammer Symbol</a>,
Previous: <a rel="previous" accesskey="p" href="Gamma-Functions.html">Gamma Functions</a>,
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<h4 class="subsection">7.19.2 Factorials</h4>
<p><a name="index-factorial-574"></a>
Although factorials can be computed from the Gamma function, using
the relation n! = \Gamma(n+1) for non-negative integer n,
it is usually more efficient to call the functions in this section,
particularly for small values of n, whose factorial values are
maintained in hardcoded tables.
<div class="defun">
— Function: double <b>gsl_sf_fact</b> (<var>unsigned int n</var>)<var><a name="index-gsl_005fsf_005ffact-575"></a></var><br>
— Function: int <b>gsl_sf_fact_e</b> (<var>unsigned int n, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005ffact_005fe-576"></a></var><br>
<blockquote><p><a name="index-factorial-577"></a>These routines compute the factorial n!. The factorial is
related to the Gamma function by n! = \Gamma(n+1).
The maximum value of n such that n! is not
considered an overflow is given by the macro <code>GSL_SF_FACT_NMAX</code>
and is 170.
<!-- exceptions: GSL_EDOM, GSL_OVRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_doublefact</b> (<var>unsigned int n</var>)<var><a name="index-gsl_005fsf_005fdoublefact-578"></a></var><br>
— Function: int <b>gsl_sf_doublefact_e</b> (<var>unsigned int n, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fdoublefact_005fe-579"></a></var><br>
<blockquote><p><a name="index-double-factorial-580"></a>These routines compute the double factorial n!! = n(n-2)(n-4) \dots.
The maximum value of n such that n!! is not
considered an overflow is given by the macro <code>GSL_SF_DOUBLEFACT_NMAX</code>
and is 297.
<!-- exceptions: GSL_EDOM, GSL_OVRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_lnfact</b> (<var>unsigned int n</var>)<var><a name="index-gsl_005fsf_005flnfact-581"></a></var><br>
— Function: int <b>gsl_sf_lnfact_e</b> (<var>unsigned int n, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005flnfact_005fe-582"></a></var><br>
<blockquote><p><a name="index-logarithm-of-factorial-583"></a>These routines compute the logarithm of the factorial of <var>n</var>,
\log(n!). The algorithm is faster than computing
\ln(\Gamma(n+1)) via <code>gsl_sf_lngamma</code> for n < 170,
but defers for larger <var>n</var>.
<!-- exceptions: none -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_lndoublefact</b> (<var>unsigned int n</var>)<var><a name="index-gsl_005fsf_005flndoublefact-584"></a></var><br>
— Function: int <b>gsl_sf_lndoublefact_e</b> (<var>unsigned int n, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005flndoublefact_005fe-585"></a></var><br>
<blockquote><p><a name="index-logarithm-of-double-factorial-586"></a>These routines compute the logarithm of the double factorial of <var>n</var>,
\log(n!!).
<!-- exceptions: none -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_choose</b> (<var>unsigned int n, unsigned int m</var>)<var><a name="index-gsl_005fsf_005fchoose-587"></a></var><br>
— Function: int <b>gsl_sf_choose_e</b> (<var>unsigned int n, unsigned int m, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005fchoose_005fe-588"></a></var><br>
<blockquote><p><a name="index-combinatorial-factor-C_0028m_002cn_0029-589"></a>These routines compute the combinatorial factor <code>n choose m</code>
= n!/(m!(n-m)!)
<!-- exceptions: GSL_EDOM, GSL_EOVRFLW -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_lnchoose</b> (<var>unsigned int n, unsigned int m</var>)<var><a name="index-gsl_005fsf_005flnchoose-590"></a></var><br>
— Function: int <b>gsl_sf_lnchoose_e</b> (<var>unsigned int n, unsigned int m, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005flnchoose_005fe-591"></a></var><br>
<blockquote><p><a name="index-logarithm-of-combinatorial-factor-C_0028m_002cn_0029-592"></a>These routines compute the logarithm of <code>n choose m</code>. This is
equivalent to the sum \log(n!) - \log(m!) - \log((n-m)!).
<!-- exceptions: GSL_EDOM -->
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_sf_taylorcoeff</b> (<var>int n, double x</var>)<var><a name="index-gsl_005fsf_005ftaylorcoeff-593"></a></var><br>
— Function: int <b>gsl_sf_taylorcoeff_e</b> (<var>int n, double x, gsl_sf_result * result</var>)<var><a name="index-gsl_005fsf_005ftaylorcoeff_005fe-594"></a></var><br>
<blockquote><p><a name="index-Taylor-coefficients_002c-computation-of-595"></a>These routines compute the Taylor coefficient x^n / n! for
<!-- {$x \ge 0$} -->
x >= 0,
<!-- {$n \ge 0$} -->
n >= 0.
<!-- exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW -->
</p></blockquote></div>
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