On a Kampé de Fériet function associated with the confluent Heun equation (Q1307649)

Properties of the Kampé de Fériet function \[ F_{1:1:0}^{1:1:1} \left[ {{a;b-1;1;} \atop {b;a;-;}} kx,x \right], \] where the parameters are complicated functions of the coefficients of the confluent Heun equation, are examined and new expressions are obtained for the Kampé de Fériet function, which occurs in the theory of confluent Heun equation and Mathieu's equation as a special case, by applying the Euler transformation for Gauss' function.