The Laplace Transform

  • Richard Beals
Part of the Graduate Texts in Mathematics book series (GTM, volume 12)


It is useful to be able to express a given function as a sum of functions of some specified type, for example as a sum of exponential functions. We have done this for smooth periodic functions: if u P, then
$$u\left( x \right) = \sum\limits_{ - \infty }^\infty {{a_n}{e^{inx}},}$$
$${a_n} = \frac{1}{{2\pi }}\int_0^{2\pi } {u\left( x \right)} {e^{ - inx}}dx.$$


Half Plane Cauchy Sequence Laplace Transform Laurent Expansion Difference Quotient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1973

Authors and Affiliations

  • Richard Beals
    • 1
  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA

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