The Krattenthaler matrix inversion formula defines lower triangular matrices 
and 
from sequences 
and 
of complex numbers such
that 
for 
by
 |
and
 |
where the product over an empty set is 1. Then 
and 
are matrix inverses (Bhatnagar
1995, pp. 16-17).
This result simplifies to the Gould and Hsu matrix inversion formula when 
, to Carlitz's 
-analog for 
(Carlitz 1972), and specialized to Bressoud's matrix
theorem (Bressoud 1983) for 
and 
(Bhatnagar 1995, p. 17).
The formula can also be extended to a summation theorem which generalizes Gosper's bibasic sum (Gasper and Rahman 1990, p. 240; Bhatnagar 1995, p. 19).
Extensions." PhD thesis. Columbus, OH: Ohio State
University, 1995.