hgs {qfratio}

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.

Value

Numeric with the same dimension with dks