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The determinant evaluation '' ` i + j + a + b
 

Summary: The determinant evaluation
det
'' ` i + j + a + b
i + a
'` 2n \Gamma i \Gamma j \Gamma a \Gamma b
n \Gamma i \Gamma a
'
0i;jm
#
=
(a + b)!(2n + 1)! m+1 (2n \Gamma m)!!m!!(m + a + b)!!(2n \Gamma m \Gamma a \Gamma b)!!a!!b!!(n \Gamma m \Gamma a \Gamma 1)!!(n \Gamma m \Gamma b \Gamma 1)!!
a!b!(2n + 1)!!(n \Gamma a)!!(n \Gamma b)!!(m + a)!!(m + b)!!(a + b)!!(2n \Gamma 2m \Gamma a \Gamma b \Gamma 1)!! ;
(Rabbit)
is just a special case of an even more general one, namely
det
0i;jM
``
a i + j +A
a i
'`

  

Source: Amdeberhan, Tewodros - Department of Mathematics, Tulane University

 

Collections: Mathematics