let be a set of orthonormal functions so [tex] (\phi _{i} , \phi_{j} ) =\delta _{ij} [/tex] then my question is if we can define:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] g(y)=\int_{0}^{\infty}dxf(x) \phi_{y} (x) [/tex]

[tex] f(x)=\int_{0}^{\infty}dy g(y) \phi_{y} (x) [/tex]

in the sense that whenever the indices i and j are discrete (i,j=1,2,3,4,5,...) you have a Kronecker's delta, wereas if i and j can vary continously (any positive real) then the scalar product becomes

[tex] (\phi _{i} , \phi_{j} ) =\delta (i-j) [/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

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!

# Orthogonal functions and integrals.

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads for Orthogonal functions integrals |
---|

I Approximating different functions |

I Equality between functions |

I Deriving a function from within an integral with a known solution |

I Integrate a function over a closed circle-like contour around an arbitrary point on a torus |

B Function rules question |

**Physics Forums | Science Articles, Homework Help, Discussion**