let be the function w(x) that only takes discrete values in the sense that is only defined for x=n being n an integer..then my question is if the integral:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int_{-\infty}^{\infty}dxw(x)f(x)[/tex]

would be equal to the sum of the serie:

[tex]\sum_{n=-\infty}^{\infty}w(n)f(n) [/tex]

if the sum and integral would be equal imply that the function

[tex]w(x)=g(x)\sum_{-\infty}^{\infty}\delta(x-n) [/tex]

thanks...

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Sum and integral

Loading...

Similar Threads for integral | Date |
---|---|

A Getting a finite result from a non-converging integral | Apr 19, 2018 |

I Decomposing a Certain Exponential Integral | Apr 12, 2018 |

How to make this integral (which does not converge) be finite? | Apr 6, 2018 |

I "Imagine" a definite integral with a finite number of discontinuties | Mar 30, 2018 |

I Improper integrals | Mar 30, 2018 |

**Physics Forums - The Fusion of Science and Community**