naginterfaces.library.specfun.gamma_vector¶
- naginterfaces.library.specfun.gamma_vector(x)[source]¶
gamma_vector
returns an array of values of the gamma function .For full information please refer to the NAG Library document for s14an
https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/s/s14anf.html
- Parameters
- xfloat, array-like, shape
The argument of the function, for .
- Returns
- ffloat, ndarray, shape
, the function values.
- ivalidint, ndarray, shape
contains the error code for , for .
No error.
is too large and positive. contains the approximate value of at the nearest valid argument. The threshold value is the same as for = 1 in
gamma()
.is too large and negative. contains zero. The threshold value is the same as for = 2 in
gamma()
.is too close to zero. contains the approximate value of at the nearest valid argument. The threshold value is the same as for = 2 in
gamma()
.is a negative integer, at which values are infinite. contains a large positive value.
- Raises
- NagValueError
- (errno )
On entry, .
Constraint: .
- Warns
- NagAlgorithmicWarning
- (errno )
On entry, at least one value of was invalid.
Check for more information.
- Notes
gamma_vector
evaluates an approximation to the gamma function for an array of arguments , for . The function is based on the Chebyshev expansion:where and uses the property . If where is integral and then it follows that:
for ,
,
for ,
,
for ,
.
There are four possible failures for this function:
if is too large, there is a danger of overflow since could become too large to be represented in the machine;
if is too large and negative, there is a danger of underflow;
if is equal to a negative integer, would overflow since it has poles at such points;
if is too near zero, there is again the danger of overflow on some machines. For small , , and on some machines there exists a range of nonzero but small values of for which is larger than the greatest representable value.
- References
NIST Digital Library of Mathematical Functions