A Potential Problem Connected With An Infinite Dock in a Running Stream
A Potential Problem Connected With An Infinite Dock in a Running Stream
Robert a Spinelli
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In the range —K-e ^*^e have that - ^ « V- 'Y-'j ■ 16 Thus as I z I = r — > c», T ° 1, j. Ra (b) Let r — > 0. We may consider only the path from any finite non-zero value of p to oo since, as r — > 0, C — > constant. Thus \.. , r. . ' ;:ai tf'-Ht . ■•;; ro/u^i: ^^i^Joi \7'' '' { :: '■ij. bzjis ITS'. ':. :'' '-xl r^::^! v. C. '■'■•';^r- •■ = y I K \ ■ iJ. Oi •rt^-^r'v ^'^•' ~ . ; 1 / LV r- ' 'J J.. ', • 1 / \ . , M . ;. A' * •f. -:-Ai N- • I '■ '. [■- ■yn - if - > ' '\ ;. I :^J -0'^ i> H job: - ...1 ?} -fKi o". -k )[e"^*-l]do = r f(a)[e"^*-l]da + r f ( a) [e"^*-l]da -00 -k -00 Jf(a; For any k, the first term Is 0(t). Choose the k large 1 enough so that we may replace f(a) by ^—r- intec:rs. L. Hence ^"'°'' In the second J -oo -k f(a)[e"^"'^-l]da ^ 0(t) + -co e-^*-l (-a) da Noxj, put at = t ; -k . -kt y -oo ^ ' 00 ^ t ^= (-t)^ -kt CO ''^ = (-t) = (-t) e e -1 -kt -kt 00 IP -r dli e — CO kt T e e - 1 -e{-kt)' kt .
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