We consider here the local zeta integral Z(s, W, W', f) for GL(2,F)x GL(2,F), which is defined from Whittaker functions
W for ([PI], [psi]), W' for ([PI]',[[psi].
Among the topics are complete elliptic integrals, the Riemann zeta function, some automatic proofs, the error function, hyper-geometric functions, Bessel-K functions, polylogarithm functions, evaluation by series, the exponential integral, confluent hyper-geometric and Whittaker functions
, and the evaluation of entries in Gradshteyn and Ryzhik employing the method of brackets.
The main objectives of this proposal are (1) to further develop the combinatorial framework in several directions which, in particular, will yield a wider family of integrable models, (2) to clarify and extend the relation between classical, quantum and stochastic integrability to a wider setting, and (3) to study thermodynamic and KPZ scaling limits of Whittaker functions
(and associated measures) and their applications.
This results in the replacement of Airy functions in Fock asymptotics with Whittaker functions.
Standard solutions of Equation (7) are Whittaker functions [M.
For the representation of the secondary field we choose the same path of integration and, as explained above, use Whittaker function W.
There is also a relation between Demazure characters and q-deformed Whittaker functions for [gl.
We now discuss how the relation between the affine grading in the Demazure crystal and the energy function can be used to derive a formula for the Demazure character using the energy function, as well as showing how they are related to nonsymmetric Macdonald polynomials and Whittaker functions.
Again, if we reduce H-function of several variables involved in (2) to the product of the whittaker functions
We are concerned with the Whittaker functions of non holomorphic Eisenstein series which are non holomorphic Siegel modular forms of degree 2.
Niwa, On generalized Whittaker functions on Siegel's upper half space of degree 2, Nagoya Math.