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and Bateman found this function as one of the solutions. Bateman denoted this function as "k" function in honor of [[Theodore von Kármán]].
The Bateman function for <math>x>0</math> is the related to the [[Confluent hypergeometric function]] of the second kind as follows
:<math>k_{\nu}(x)=\frac{e^{-x}}{\Gamma\left(1+\frac{1}{2}\nu\right)} U\left(-\frac{1}{2}\nu,0,2x\right), \quad x>0.</math>
This is not to be confused with another function of the same name which is used in Pharmacokinetics.
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