dirac_delta( x )

The Dirac delta function in SageMath. Defined by

\[ \delta(x) = \frac{ 1 }{ 2\pi } \int_{-\infty}^\infty dk \: e^{ ikx } \]

with the properties

\[ \delta(x) = \begin{cases} \ 0 \ \ , \ x \ne 0 \\ \infty \ , \ x = 0 \end{cases} \quad \quad \quad \quad \quad \int_{-\infty}^\infty dx \: \delta(x) = 1 \]

Related to heaviside by

\[ \frac{ d }{ dx } H(x) = \delta(x) \]

Special values:

Related functions:   heaviside   spike_function

Function category: generalized functions sagemath-docs