stdlib_specialfunctions_gamma#

See also the specification page: stdlib_specialfunctions_gamma.

stdlib_specialfunctions_gamma (module)#

Interfaces

gamma (interface)#

gamma (interface)

Gamma function for integer and complex numbers

Procedures:

log_gamma (interface)#

log_gamma (interface)

Logarithm of gamma function

Procedures:

log_factorial (interface)#

log_factorial (interface)

Logarithm of factorial n!, integer variable

Procedures:

lower_incomplete_gamma (interface)#

lower_incomplete_gamma (interface)

Lower incomplete gamma function

Procedures:

log_lower_incomplete_gamma (interface)#

log_lower_incomplete_gamma (interface)

Logarithm of lower incomplete gamma function

Procedures:

upper_incomplete_gamma (interface)#

upper_incomplete_gamma (interface)

Upper incomplete gamma function

Procedures:

log_upper_incomplete_gamma (interface)#

log_upper_incomplete_gamma (interface)

Logarithm of upper incomplete gamma function

Procedures:

regularized_gamma_p (interface)#

regularized_gamma_p (interface)

Regularized (normalized) lower incomplete gamma function, P

Procedures:

regularized_gamma_q (interface)#

regularized_gamma_q (interface)

Regularized (normalized) upper incomplete gamma function, Q

Procedures:

beta (interface)#

beta (interface)

Beta function

Procedures:

log_beta (interface)#

log_beta (interface)

Logarithm of beta function

Procedures:

incomplete_beta (interface)#

incomplete_beta (interface)

Regularized incomplete beta function I_x(a,b)

Procedures:

Procedures

gamma_iint8 (function)#

impure elemental function gamma_iint8(z) -> res
Arguments:
zinteger(kind=int8), intent(in)
Returns:
resinteger(kind=int8)

gamma_iint16 (function)#

impure elemental function gamma_iint16(z) -> res
Arguments:
zinteger(kind=int16), intent(in)
Returns:
resinteger(kind=int16)

gamma_iint32 (function)#

impure elemental function gamma_iint32(z) -> res
Arguments:
zinteger(kind=int32), intent(in)
Returns:
resinteger(kind=int32)

gamma_iint64 (function)#

impure elemental function gamma_iint64(z) -> res
Arguments:
zinteger(kind=int64), intent(in)
Returns:
resinteger(kind=int64)

gamma_csp (function)#

impure elemental function gamma_csp(z) -> res
Arguments:
zcomplex(kind=sp), intent(in)
Returns:
rescomplex(kind=sp)

gamma_cdp (function)#

impure elemental function gamma_cdp(z) -> res
Arguments:
zcomplex(kind=dp), intent(in)
Returns:
rescomplex(kind=dp)

l_gamma_iint8 (function)#

impure elemental function l_gamma_iint8(z) -> res
Arguments:
zinteger(kind=int8), intent(in)
Returns:
resreal(kind=dp)

l_gamma_iint16 (function)#

impure elemental function l_gamma_iint16(z) -> res
Arguments:
zinteger(kind=int16), intent(in)
Returns:
resreal(kind=dp)

l_gamma_iint32 (function)#

impure elemental function l_gamma_iint32(z) -> res
Arguments:
zinteger(kind=int32), intent(in)
Returns:
resreal(kind=dp)

l_gamma_iint64 (function)#

impure elemental function l_gamma_iint64(z) -> res
Arguments:
zinteger(kind=int64), intent(in)
Returns:
resreal(kind=dp)

l_gamma_csp (function)#

impure elemental function l_gamma_csp(z) -> res
Arguments:
zcomplex(kind=sp), intent(in)
Returns:
rescomplex(kind=sp)

l_gamma_cdp (function)#

impure elemental function l_gamma_cdp(z) -> res
Arguments:
zcomplex(kind=dp), intent(in)
Returns:
rescomplex(kind=dp)

l_factorial_iint8 (function)#

impure elemental function l_factorial_iint8(n) -> res
Arguments:
ninteger(kind=int8), intent(in)
Returns:
resreal(kind=sp)

l_factorial_iint16 (function)#

impure elemental function l_factorial_iint16(n) -> res
Arguments:
ninteger(kind=int16), intent(in)
Returns:
resreal(kind=sp)

l_factorial_iint32 (function)#

impure elemental function l_factorial_iint32(n) -> res
Arguments:
ninteger(kind=int32), intent(in)
Returns:
resreal(kind=sp)

l_factorial_iint64 (function)#

impure elemental function l_factorial_iint64(n) -> res
Arguments:
ninteger(kind=int64), intent(in)
Returns:
resreal(kind=sp)

ingamma_low_rsp (function)#

impure elemental function ingamma_low_rsp(p, x) -> res
Arguments:
preal(kind=sp), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

ingamma_low_rdp (function)#

impure elemental function ingamma_low_rdp(p, x) -> res
Arguments:
preal(kind=dp), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

ingamma_low_iint8sp (function)#

impure elemental function ingamma_low_iint8sp(p, x) -> res
Arguments:
pinteger(kind=int8), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

ingamma_low_iint8dp (function)#

impure elemental function ingamma_low_iint8dp(p, x) -> res
Arguments:
pinteger(kind=int8), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

ingamma_low_iint16sp (function)#

impure elemental function ingamma_low_iint16sp(p, x) -> res
Arguments:
pinteger(kind=int16), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

ingamma_low_iint16dp (function)#

impure elemental function ingamma_low_iint16dp(p, x) -> res
Arguments:
pinteger(kind=int16), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

ingamma_low_iint32sp (function)#

impure elemental function ingamma_low_iint32sp(p, x) -> res
Arguments:
pinteger(kind=int32), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

ingamma_low_iint32dp (function)#

impure elemental function ingamma_low_iint32dp(p, x) -> res
Arguments:
pinteger(kind=int32), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

ingamma_low_iint64sp (function)#

impure elemental function ingamma_low_iint64sp(p, x) -> res
Arguments:
pinteger(kind=int64), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

ingamma_low_iint64dp (function)#

impure elemental function ingamma_low_iint64dp(p, x) -> res
Arguments:
pinteger(kind=int64), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

l_ingamma_low_rsp (function)#

impure elemental function l_ingamma_low_rsp(p, x) -> res
Arguments:
preal(kind=sp), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

l_ingamma_low_rdp (function)#

impure elemental function l_ingamma_low_rdp(p, x) -> res
Arguments:
preal(kind=dp), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

l_ingamma_low_iint8sp (function)#

impure elemental function l_ingamma_low_iint8sp(p, x) -> res
Arguments:
pinteger(kind=int8), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

l_ingamma_low_iint8dp (function)#

impure elemental function l_ingamma_low_iint8dp(p, x) -> res
Arguments:
pinteger(kind=int8), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

l_ingamma_low_iint16sp (function)#

impure elemental function l_ingamma_low_iint16sp(p, x) -> res
Arguments:
pinteger(kind=int16), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

l_ingamma_low_iint16dp (function)#

impure elemental function l_ingamma_low_iint16dp(p, x) -> res
Arguments:
pinteger(kind=int16), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

l_ingamma_low_iint32sp (function)#

impure elemental function l_ingamma_low_iint32sp(p, x) -> res
Arguments:
pinteger(kind=int32), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

l_ingamma_low_iint32dp (function)#

impure elemental function l_ingamma_low_iint32dp(p, x) -> res
Arguments:
pinteger(kind=int32), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

l_ingamma_low_iint64sp (function)#

impure elemental function l_ingamma_low_iint64sp(p, x) -> res
Arguments:
pinteger(kind=int64), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

l_ingamma_low_iint64dp (function)#

impure elemental function l_ingamma_low_iint64dp(p, x) -> res
Arguments:
pinteger(kind=int64), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

ingamma_up_rsp (function)#

impure elemental function ingamma_up_rsp(p, x) -> res
Arguments:
preal(kind=sp), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

ingamma_up_rdp (function)#

impure elemental function ingamma_up_rdp(p, x) -> res
Arguments:
preal(kind=dp), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

ingamma_up_iint8sp (function)#

impure elemental function ingamma_up_iint8sp(p, x) -> res
Arguments:
pinteger(kind=int8), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

ingamma_up_iint8dp (function)#

impure elemental function ingamma_up_iint8dp(p, x) -> res
Arguments:
pinteger(kind=int8), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

ingamma_up_iint16sp (function)#

impure elemental function ingamma_up_iint16sp(p, x) -> res
Arguments:
pinteger(kind=int16), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

ingamma_up_iint16dp (function)#

impure elemental function ingamma_up_iint16dp(p, x) -> res
Arguments:
pinteger(kind=int16), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

ingamma_up_iint32sp (function)#

impure elemental function ingamma_up_iint32sp(p, x) -> res
Arguments:
pinteger(kind=int32), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

ingamma_up_iint32dp (function)#

impure elemental function ingamma_up_iint32dp(p, x) -> res
Arguments:
pinteger(kind=int32), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

ingamma_up_iint64sp (function)#

impure elemental function ingamma_up_iint64sp(p, x) -> res
Arguments:
pinteger(kind=int64), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

ingamma_up_iint64dp (function)#

impure elemental function ingamma_up_iint64dp(p, x) -> res
Arguments:
pinteger(kind=int64), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

l_ingamma_up_rsp (function)#

impure elemental function l_ingamma_up_rsp(p, x) -> res
Arguments:
preal(kind=sp), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

l_ingamma_up_rdp (function)#

impure elemental function l_ingamma_up_rdp(p, x) -> res
Arguments:
preal(kind=dp), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

l_ingamma_up_iint8sp (function)#

impure elemental function l_ingamma_up_iint8sp(p, x) -> res
Arguments:
pinteger(kind=int8), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

l_ingamma_up_iint8dp (function)#

impure elemental function l_ingamma_up_iint8dp(p, x) -> res
Arguments:
pinteger(kind=int8), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

l_ingamma_up_iint16sp (function)#

impure elemental function l_ingamma_up_iint16sp(p, x) -> res
Arguments:
pinteger(kind=int16), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

l_ingamma_up_iint16dp (function)#

impure elemental function l_ingamma_up_iint16dp(p, x) -> res
Arguments:
pinteger(kind=int16), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

l_ingamma_up_iint32sp (function)#

impure elemental function l_ingamma_up_iint32sp(p, x) -> res
Arguments:
pinteger(kind=int32), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

l_ingamma_up_iint32dp (function)#

impure elemental function l_ingamma_up_iint32dp(p, x) -> res
Arguments:
pinteger(kind=int32), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

l_ingamma_up_iint64sp (function)#

impure elemental function l_ingamma_up_iint64sp(p, x) -> res
Arguments:
pinteger(kind=int64), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

l_ingamma_up_iint64dp (function)#

impure elemental function l_ingamma_up_iint64dp(p, x) -> res
Arguments:
pinteger(kind=int64), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

regamma_p_rsp (function)#

impure elemental function regamma_p_rsp(p, x) -> res
Arguments:
preal(kind=sp), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

regamma_p_rdp (function)#

impure elemental function regamma_p_rdp(p, x) -> res
Arguments:
preal(kind=dp), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

regamma_p_iint8sp (function)#

impure elemental function regamma_p_iint8sp(p, x) -> res
Arguments:
pinteger(kind=int8), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

regamma_p_iint8dp (function)#

impure elemental function regamma_p_iint8dp(p, x) -> res
Arguments:
pinteger(kind=int8), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

regamma_p_iint16sp (function)#

impure elemental function regamma_p_iint16sp(p, x) -> res
Arguments:
pinteger(kind=int16), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

regamma_p_iint16dp (function)#

impure elemental function regamma_p_iint16dp(p, x) -> res
Arguments:
pinteger(kind=int16), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

regamma_p_iint32sp (function)#

impure elemental function regamma_p_iint32sp(p, x) -> res
Arguments:
pinteger(kind=int32), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

regamma_p_iint32dp (function)#

impure elemental function regamma_p_iint32dp(p, x) -> res
Arguments:
pinteger(kind=int32), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

regamma_p_iint64sp (function)#

impure elemental function regamma_p_iint64sp(p, x) -> res
Arguments:
pinteger(kind=int64), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

regamma_p_iint64dp (function)#

impure elemental function regamma_p_iint64dp(p, x) -> res
Arguments:
pinteger(kind=int64), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

regamma_q_rsp (function)#

impure elemental function regamma_q_rsp(p, x) -> res
Arguments:
preal(kind=sp), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

regamma_q_rdp (function)#

impure elemental function regamma_q_rdp(p, x) -> res
Arguments:
preal(kind=dp), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

regamma_q_iint8sp (function)#

impure elemental function regamma_q_iint8sp(p, x) -> res
Arguments:
pinteger(kind=int8), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

regamma_q_iint8dp (function)#

impure elemental function regamma_q_iint8dp(p, x) -> res
Arguments:
pinteger(kind=int8), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

regamma_q_iint16sp (function)#

impure elemental function regamma_q_iint16sp(p, x) -> res
Arguments:
pinteger(kind=int16), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

regamma_q_iint16dp (function)#

impure elemental function regamma_q_iint16dp(p, x) -> res
Arguments:
pinteger(kind=int16), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

regamma_q_iint32sp (function)#

impure elemental function regamma_q_iint32sp(p, x) -> res
Arguments:
pinteger(kind=int32), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

regamma_q_iint32dp (function)#

impure elemental function regamma_q_iint32dp(p, x) -> res
Arguments:
pinteger(kind=int32), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

regamma_q_iint64sp (function)#

impure elemental function regamma_q_iint64sp(p, x) -> res
Arguments:
pinteger(kind=int64), intent(in)
xreal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

regamma_q_iint64dp (function)#

impure elemental function regamma_q_iint64dp(p, x) -> res
Arguments:
pinteger(kind=int64), intent(in)
xreal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

beta_rsp (function)#

elemental function beta_rsp(a, b) -> res
Arguments:
areal(kind=sp), intent(in)
breal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

beta_rdp (function)#

elemental function beta_rdp(a, b) -> res
Arguments:
areal(kind=dp), intent(in)
breal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

log_beta_rsp (function)#

elemental function log_beta_rsp(a, b) -> res
Arguments:
areal(kind=sp), intent(in)
breal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

log_beta_rdp (function)#

elemental function log_beta_rdp(a, b) -> res
Arguments:
areal(kind=dp), intent(in)
breal(kind=dp), intent(in)
Returns:
resreal(kind=dp)

incomplete_beta_rsp (function)#

elemental function incomplete_beta_rsp(x, a, b) -> res
Arguments:
xreal(kind=sp), intent(in)
areal(kind=sp), intent(in)
breal(kind=sp), intent(in)
Returns:
resreal(kind=sp)

incomplete_beta_rdp (function)#

elemental function incomplete_beta_rdp(x, a, b) -> res
Arguments:
xreal(kind=dp), intent(in)
areal(kind=dp), intent(in)
breal(kind=dp), intent(in)
Returns:
resreal(kind=dp)
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