From: A quasi-analytical solution of homogeneous extended surfaces heat diffusion equation
Functions | Transform functions |
---|---|
f(x)= | F(k) |
af 1(x) + bf 2(x) | F(k) = aF 1(k) + bF 2(k) |
\( \frac{df}{dx} \) | F(k) = (k + 1)F(k + 1) |
\( \frac{d^2f}{dx^2} \) | F(k) = (k + 1)(k + 2)F(k + 2) |
x n | \( F(k)=\delta \left(k-n\right)=\left\{\begin{array}{c}1\kern0.75em si\kern0.75em k=n\\ {}0\kern0.75em si\kern0.5em k\ne n\end{array}\right. \) |
exp(λx) | \( F(k)=\frac{\lambda^k}{k!} \) |
f 1(x)f 2(x) | \( F(k)=\sum_{l=0}^k{F}_1(l){F}_2\left(k-l\right) \) |
f 1(x)f 2(x)f 3(x) | \( F(k)=\sum_{h=0}^k\sum_{l=0}^h{F}_1(l){F}_2\left(h-l\right){F}_3\left(k-h\right) \) |