## Documentation for module gamma Calculation of the incomplete Gamma function F_n(t) for multi-center integrals over Cartesian Gaussian functions.

source: gamma.F
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#### public Subroutines/Functions:

Deallocate the table of F_n(t) values.
SUBROUTINE
fgamma_0 (nmax, t, f)
Calculation of the incomplete Gamma function F(t) for multicenter integrals over Gaussian functions. f returns a vector with all F_n(t) values for 0 <= n <= nmax.
fgamma_ref (nmax, t)
Calculation of the incomplete Gamma function F_n(t) using a spherical Bessel function expansion. fgamma_ref returns a vector with all F_n(t) values for 0 <= n <= nmax. For t values greater than 50 an asymptotic formula is used. This function is expected to return accurate F_n(t) values for any combination of n and t, but the calculation is slow and therefore the function may only be used for a pretabulation of F_n(t) values or for reference calculations.
SUBROUTINE
init_md_ftable (nmax)
Initalize a table of F_n(t) values in the range 0 <= t <= 12 with a stepsize of 0.1 up to n equal to nmax for the Taylor series expansion used by McMurchie-Davidson (MD).

#### SUBROUTINEdeallocate_md_ftable()^

Deallocate the table of F_n(t) values.

#### SUBROUTINEfgamma_0(nmax, t, f)^

Calculation of the incomplete Gamma function F(t) for multicenter integrals over Gaussian functions. f returns a vector with all F_n(t) values for 0 <= n <= nmax.

##### Arguments:
 INTEGER, INTENT(in) :: nmax ... REAL(dp), INTENT(in) :: t ... REAL(dp), INTENT(out) :: f(0:nmax) ...

#### FUNCTIONfgamma_ref(nmax, t)^

Calculation of the incomplete Gamma function F_n(t) using a spherical Bessel function expansion. fgamma_ref returns a vector with all F_n(t) values for 0 <= n <= nmax. For t values greater than 50 an asymptotic formula is used. This function is expected to return accurate F_n(t) values for any combination of n and t, but the calculation is slow and therefore the function may only be used for a pretabulation of F_n(t) values or for reference calculations.

 Return Value :: REAL(dp)
##### Arguments:
 INTEGER, INTENT(in) :: nmax ... REAL(dp), INTENT(in) :: t ...

#### SUBROUTINEinit_md_ftable(nmax)^

Initalize a table of F_n(t) values in the range 0 <= t <= 12 with a stepsize of 0.1 up to n equal to nmax for the Taylor series expansion used by McMurchie-Davidson (MD).

##### Arguments:
 INTEGER, INTENT(in) :: nmax ...