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 New Online Book! Handbook of Mathematical Functions (AMS55) Conversion & Calculation Home >> Reference Information Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables (AMS55) Purchase the electronic edition of this book in Adobe PDF format! FIRST | PREVIOUS | NEXT | LAST | CONTENTS | PAGE | ABOUT | SMALL | MEDIUM | LARGE Below is the OCR-scanned text from this page: LAPLACE TRANSFORMS f(5) p ( t ) 1 5 - t+a 29.3.126 easEl (us) (u>O) For the definition of the Laplace-Stieltjcs transform see [29.7]. In practice, Laplace-Stieltjes transforms are often written as ordinary Laplace transforms involving Dirac's delta function 6(t). 1 29.3.127 --sea8El(as) (u>O) the derivative of the unit step function, du(t) =s(t) dt, so that JIa dzr(t)= Lm s(t)dt= {; ;s;. Tlic corrcspondcncc 29.4.2, Tor instance), then 1 5 - ( t + C 1 29.3.128 al-neuSE,(as) (a>O;n=O, 1 , 2 , . . .) 5 - ( t +a) 1 5 - t2+ 1 29.3.129 b-Si(s)] cos s+Ci(s) sin s 29.4. Table of Laplace-Stieltjes Transforms d4 W ) 29.4.3 29.4.4 29.4.5 29.4.6 2 u(t-nk) n=O m 1 l+e-ks 1 sinh ks % (-l)"u(t--nk) n=O 2 2 u[t-(2n+l)k] n=O m 2 2 (-1)"u[t-(2n+l)k] n=O m u(t)+2 C (-1)"u(t-2nk) n=l 29.4.7 tanh ks (k>O) 29.4.8 29.4.9 (k>O) 1 sinh (ks+a) e-hs sinh (ks+a) (O