hgs: Calculate hypergeometric series
In qfratio: Moments and Distributions of Ratios of Quadratic Forms Using Recursion

hgs	R Documentation

Calculate hypergeometric series

Description

These internal functions calculate (summands of) hypergeometric series.

hgs_1d() calculates the hypergeometric series c \frac{(a_1)_i}{(b)_i} d_{i}

hgs_2d() calculates the hypergeometric series c \frac{(a_1)_i (a_2)_j}{(b)_{i+j}} d_{i, j}

hgs_3d() calculates the hypergeometric series c \frac{(a_1)_i (a_2)_j (a_3)_k}{(b)_{i+j+k}} d_{i, j, k}

Usage

hgs_1d(dks, a1, b, lconst = 0)

hgs_2d(dks, a1, a2, b, lconst = 0)

hgs_3d(dks, a1, a2, a3, b, lconst = 0)

Arguments

`dks`	`(m + 1)` vector for `d_{i}`, `(m + 1) * (m + 1)` square matrix for `d_{i,j}`, or `(m + 1) * (m + 1) * (m + 1)` array for `d_{i,j,k}` (`i, j, k = 0, 1, \dots m`)
`a1`, `a2`, `a3`	Numerator parameters
`b`	Denominator parameter
`lconst`	Scalar `\log c`

Details

The denominator parameter b is assumed positive, whereas the numerator parameters can be positive or negative. The signs of the latter will be reflected in the result.