Lambda functions for dipole applications

Lambda functions, a class of functions resembling the Bessel functions, have many applications in antenna theory. This paper shows their application to describe some of the properties of dipoles. The field components of an electrically short dipole are usually expressed in terms of the inverse distance
1/r
and its powers
1/r^{2}
and
1/r^{3}
. It is shown that the functions containing
r
are Lambda functions. The field components can then be concisely expressed in Lambda notation and the range dependence is easily determined from standard tables and graphs of the Lambda functions. The Lambda characterization of the field arises from the vector potential being itself a simple Lambda function. Lambda functions then enter into applications of short dipoles and simplify the descriptions. Examples are given in respect of mutual coupling, gain formulas, and lines of force. The paper contains a short account of the definitions and properties of the Lambda functions required for the dipole applications.