We solve the equation of the title for q = 3 and, partially, for q = 2. These are the only prime values of q for which there exist integer solutions. Our arguments are based upon off-diagonal Padé approximation to the binomial function.

We prove an existence of a unique solution of an exponential martingale equation in the class of BMO martingales. The solution is used to characterize optimal martingale measures.

the purpose of this paper is to analyze in detail a special nonlinear partial differentialequation (npde) of the second order which is important in physical, chemical and technicalapplications. the present npde describes nonlinear diffusion and is of interest in several partsof physics, chemistry and engineering problems alike. since nature is not linear intrinsicallythe nonlinear case is there...

in this paper , numerical solotion of abel's integral equationby using the taylor expanssion of the unknown functionvia collection method based on sinc is considered...