GNU Scientific Library Reference Manual - Third Edition (v1.12)by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi Paperback (6"x9"), 592 pages, 60 figures ISBN 0954612078 RRP £24.95 ($39.95) |

### 7.19.2 Factorials

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.

__Function:__double**gsl_sf_fact***(unsigned int*`n`)__Function:__int**gsl_sf_fact_e***(unsigned int*`n`, gsl_sf_result *`result`)- 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
`GSL_SF_FACT_NMAX`

and is 170.

__Function:__double**gsl_sf_doublefact***(unsigned int*`n`)__Function:__int**gsl_sf_doublefact_e***(unsigned int*`n`, gsl_sf_result *`result`)- 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
`GSL_SF_DOUBLEFACT_NMAX`

and is 297.

__Function:__double**gsl_sf_lnfact***(unsigned int*`n`)__Function:__int**gsl_sf_lnfact_e***(unsigned int*`n`, gsl_sf_result *`result`)- These routines compute the logarithm of the factorial of
`n`, \log(n!). The algorithm is faster than computing \ln(\Gamma(n+1)) via`gsl_sf_lngamma`

for n < 170, but defers for larger`n`.

__Function:__double**gsl_sf_lndoublefact***(unsigned int*`n`)__Function:__int**gsl_sf_lndoublefact_e***(unsigned int*`n`, gsl_sf_result *`result`)- These routines compute the logarithm of the double factorial of
`n`, \log(n!!).

__Function:__double**gsl_sf_choose***(unsigned int*`n`, unsigned int`m`)__Function:__int**gsl_sf_choose_e***(unsigned int*`n`, unsigned int`m`, gsl_sf_result *`result`)- These routines compute the combinatorial factor
`n choose m`

= n!/(m!(n-m)!)

__Function:__double**gsl_sf_lnchoose***(unsigned int*`n`, unsigned int`m`)__Function:__int**gsl_sf_lnchoose_e***(unsigned int*`n`, unsigned int`m`, gsl_sf_result *`result`)- These routines compute the logarithm of
`n choose m`

. This is equivalent to the sum \log(n!) - \log(m!) - \log((n-m)!).

__Function:__double**gsl_sf_taylorcoeff***(int*`n`, double`x`)__Function:__int**gsl_sf_taylorcoeff_e***(int*`n`, double`x`, gsl_sf_result *`result`)- These routines compute the Taylor coefficient x^n / n! for x >= 0, n >= 0.

ISBN 0954612078 | GNU Scientific Library Reference Manual - Third Edition (v1.12) | See the print edition |