Polygamma

Element-wise polygamma function: the (n+1)-th derivative of the log-gamma function. For n = 0 this is the digamma function; for n = 1, trigamma() dispatches here.

Usage

nv_polygamma(n, x)

Arguments

n, x

(arrayish)
Order of the polygamma function and the value to evaluate it at. n typically holds non-negative whole numbers. Can be any numeric data type: the two are promoted to a common data type and that is then converted to the default float data type (see default_dtypes()) where it is not a float already, since a float is all prim_polygamma() takes. An R value assumes the other operand's data type within its data type category, and settles on the default float when neither has one. Scalars are broadcast to the shape of the other, so nv_polygamma(1, x) works for any float x.

Value

(arrayish)
Has the inputs' broadcast shape, and their common data type – or the default float data type (see default_dtypes()) where that was an integer one.

The trigamma() generic

trigamma(x) is nv_polygamma(1L, x).

See also

prim_polygamma() for the underlying primitive.

Examples

# the R `1` is built at `x`'s float data type and broadcast
x <- nv_array(c(0.5, 1, 2, 5))
nv_polygamma(1, x) # trigamma
#> AnvlArray
#>  4.9348
#>  1.6449
#>  0.6449
#>  0.2213
#> [ CPUf32{4} ]