(adsbygoogle = window.adsbygoogle || []).push({}); Integral equality....

let be a and b real numbers..and let be the integral...

[tex]\int_{-\infty}^{\infty}dxf(x)x^{a}\int_{-\infty}^{\infty}g(x+y)y^{ib}=0 [/tex] so if this is zero also will be its conjugate:

[tex]\int_{-\infty}^{\infty}dxf(x)x^{a}\int_{-\infty}^{\infty}g(x+y)y^{-ib}=0 [/tex] now let,s suppose we would have that (1-a,-b) is also a zero so:

[tex]\int_{-\infty}^{\infty}dxf(x)x^{1-a}\int_{-\infty}^{\infty}g(x+y)y^{-ib}=0 [/tex] then my conclusion is that 1-a=a a=1/2 and there is no other solution.. :zzz:

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

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

# Integral equality

Loading...

Similar Threads - Integral equality | Date |
---|---|

I Equality of two particular solutions of 2nd order linear ODE | Nov 25, 2017 |

I Why this triple integral equals zero? | Sep 5, 2016 |

B Making a definite integral equal and indefinite integral? | May 24, 2016 |

Doesn't this integral equal zero? | Dec 10, 2013 |

How to show integral equal to hypergeometric function? | Oct 3, 2013 |

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