chapter
Theorem 9.4(Balanced Dixon Formula).
Pages 10

F. J. W. Whipple [Whipple 25] in 1925, but both are transformations of the above formulas due to Dixon.

Sn (a1, a2, b1, b2) = n∑

( n

k

) [a1]k [a2]k [b1]n−k [b2]n−k (−1)k (9.4)

are independent of interchanging a1 and a2 or b1 and b2, and of reversing the direction of summation, except for the factor (−1)n, which depends on the interchange of the pair of sets {a1, a2} and {b1, b2}.