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
.