On the class of A1 numbers: Definition, numerical modeling, domain of existence and application

The relation A 1 = A 1- -A 1+ is exploited to advance the class of positive real numbers A 1 by means of the ones A 1- and A 1+ . The latter are defined with the help of the positive purely imaginary zeros of a complex Kummer function of specially picked out parameters. A method is elaborated for counting the numerical equivalents of A 1- and A 1+ (of A 1 ). Tables and graphs illustrate the outcomes of computations. The limits of the existence domains of each of the three kinds of numbers are found, too. A formula for calculation of the differential phase shift produced by the circular waveguide with azimuthally magnetized ferrite which sustains normal TE 01 mode is suggested, employing the quantities A 1 .