Laplace Transforms f(x) = e^(-xt) g(t) dt (Laplace Transform) f(x) = e^(-xt) g(t) d(t) (Laplace-Stieltjes Transform) f2(x) = L{L{g(t)}} = g(t)/(x+t) dt (Stieltjes Transform)
Fourier Transforms f(x) = 1/(2) g(t) e^(i tx) dt (Fourier Transform) f(x) = (2/) g(x) cos(xt) dt (Cosine Transform) f(x) = (2/) g(x) sin(xt) dt (Sine Transform)
Power Series Transform
f(x) = (k=0..) g(k) x^k
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Laplace
Transforms
f(x) = 
e^(-xt) g(t) dt (Laplace Transform)
(t) (Laplace-Stieltjes
Transform)
(2
)
g(t) e^(i tx) dt 
(k=0..
)
g(k) x^k
