Generalization of a Quadratic Transformation Formula due to Gauss

Table 1

𝑗	−2	−1	0	1	2
𝐷𝑗	1−((4𝑛(𝑎+𝑛))/((𝑐−1)(2𝑐−2𝑎−3)))	1	1	1	1−((4𝑛(𝑎+𝑛))/((𝑐+1)(2𝑐−2𝑎+1)))
𝐸𝑗	−1/(𝑐−1)	−1/(2𝑐−1)	0	1/(2𝑐+1)	1/(𝑐+1)