Remarks on the Whittaker functions

The probability density function for the output of an analog cross-correlator with correlated bandpass inputs as well as temperature field due to time-dependent continuously operating heat sources can be expressed in terms of the Whittaker functions, W_λ,μ(x). It is shown that the Whittaker function can be expressed in terms of derivatives of incomplete Gamma function, G{cyrillic}(α,x). This relation is further exploited to derive some new relations of W_λ,μ(x) with other well-known special functions, in addition to the known representations of the Whittaker function. Furthermore, some infinite series of the Whittaker functions are expressed in terms of the elementary functions, incomplete Gamma functions, error functions and other special functions.