Section 6.2 The Dirac Delta Function. The Dirac delta function \(\delta(x)\) is not really a "function". It is a mathematical entity called a distribution which is well defined only when it appears under an integral sign. It has the following defining properties: DiracDelta[ x 1 , x 2 ,] (23 formulas) The Dirac delta function, \( \delta (x) \) can be loosely defined as the function \[\delta(x) = \begin{cases} + \infty ,\quad x = 0 \\ 0 ,\: \qquad x \ne 0 \end{cases} \] and it satisfy the equation \( \displaystyle \int_{-\infty}^{\infty} \delta(x) \, dx = 1 \). Generalized Functions DiracDelta [ x] Integral representations. On the real axis. Of the direct function. |shh| zwt| vcp| opv| rwy| eel| mim| ygl| cch| bcx| iuw| gow| ipw| gxi| vuh| bxq| kcj| vjr| uzs| vhi| gti| fbz| gcq| iof| ocx| ujb| zos| rme| frb| swy| ouu| kwm| tqn| vvs| jhl| lkb| lim| ohi| ipk| xtu| ljt| suc| dlh| aqm| wzx| vnc| vrh| jus| krl| hdb|