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Vandermonde sum

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1: 17.6 ϕ 1 2 Function
First q -Chu–Vandermonde Sum
Second q -Chu–Vandermonde Sum
Nonterminating Form of the q -Vandermonde Sum
2: 15.4 Special Cases
Chu–Vandermonde Identity
Dougall’s Bilateral Sum
15.4.25 n = - Γ ( a + n ) Γ ( b + n ) Γ ( c + n ) Γ ( d + n ) = π 2 sin ( π a ) sin ( π b ) Γ ( c + d - a - b - 1 ) Γ ( c - a ) Γ ( d - a ) Γ ( c - b ) Γ ( d - b ) .
3: 1.3 Determinants
1.3.4 det [ a j k ] = = 1 n a j A j .
1.3.9 det [ a j k ] 2 ( k = 1 n a 1 k 2 ) ( k = 1 n a 2 k 2 ) ( k = 1 n a n k 2 ) .
for every distinct pair of j , k , or when one of the factors k = 1 n a j k 2 vanishes. …
Vandermonde Determinant or Vandermondian
1.3.19 j , k = - | a j , k - δ j , k |
4: Bibliography D
  • K. Dilcher (1996) Sums of products of Bernoulli numbers. J. Number Theory 60 (1), pp. 23–41.
  • A. M. Din (1981) A simple sum formula for Clebsch-Gordan coefficients. Lett. Math. Phys. 5 (3), pp. 207–211.
  • J. Dougall (1907) On Vandermonde’s theorem, and some more general expansions. Proc. Edinburgh Math. Soc. 25, pp. 114–132.
  • T. M. Dunster (1990a) Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter. SIAM J. Math. Anal. 21 (4), pp. 995–1018.