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In this paper, an explicit error bound is obtained for an expansion of the Whittaker function,      W k , m ( z ) {W_{k,m}}(z)      , in series of parabolic cylinder functions. It is also shown that the Whittaker function may be asymptotically represented as the sum of two products where one product involves a parabolic cylinder function and the other product involves the first-order derivative of this function.

Series expansions of 𝑊_{𝑘,𝑚}(𝑍) involving parabolic cylinder functions