A Convergent Asymptotic Representation for Integrals
A Convergent Asymptotic Representation for Integrals
Joel Franklin
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Here we have used the fact that Inserting (2U) into (23) and integrating the first n terms, we find for the in- tegral in (23) the representation (25) - 00 n«l r C*r')/«-'*^'^«''(FW*«„ where (26) R^ y e-^^/P r (' ' k " ^) ?^''(|)dl(t). o From (21) and (25) it follows that the theorem will be proved when it has been shown that R -^ as n -!> oo« n For the sake of convenience, put co(t) - I(tp)j then co(t) is of the bounded variation in each finite t-interval, and |oo(t)| . we may write the second... summation in (28) in the form (29) i^|
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