Abstract
We derive new approximate representations of the Lommel functions in terms of the Scorer function and approximate representations of the first derivative of the Lommel functions in terms of the derivative of the Scorer function. Using the same method, we obtain previously known approximate representations of the Nicholson type for Bessel functions and their first derivatives. We study also for what values of the parameters our representations have reasonable accuracy.
Highlights
The approximate representation (4.2) of the Lommel function s0,n for n 1 in terms of the Scorer function Gi is similar to the following formula (11.11.17) in [5]: A−ν
We present the plots of the functions of the variable t, which appear in the left- and right-hand sides of formulae (2.1), (2.2), (3.8) and (5.3) for various values of n
— representations (2.1), (2.2), (3.8) and (5.3) have reasonable accuracy starting from relatively small values of n or t
Summary
We derive new approximate representations of the Lommel functions in terms of the Scorer function and approximate representations of the first derivative of the Lommel functions in terms of the derivative of the Scorer function. We study for what values of the parameters our representations have reasonable accuracy
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