Abstract :
We derive new recursive formulas for principal series Whittaker functions, of both fundamental and
class one type, on GL(n,R). These formulas relate such Whittaker functions to their counterparts on
GL(n−1,R), instead of on GL(n − 2,R) as has been the case in numerous earlier studies. In the particular
case n = 3, and for certain special values of the eigenvalues, our formulas are seen to resemble
classical summation formulas, due to Gegenbauer, for Bessel functions. To illuminate this resemblance we
also derive, in this work, formulas for certain special values of GL(3,R) fundamental Whittaker functions.
These formulas may be understood as analogs of expressions derived by Bump and Friedberg for class one
Whittaker functions on GL(3,R).
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