I'm looking for a mathematical function that...

[eleteroboltz]

Hi guys,

 

I'm looking for a function [latex] b(x,y) [/latex] that satisfies:

 

[latex] \int_0^L \int_0^H b(x,y) \, dx \, dy = 0[/latex]

 

and

 

[latex] \int_0^L \int_0^H b(x,y) \cos \left(\frac{n \, \pi \, x}{L} \right) \cos \left(\frac{m \, \pi \, y}{H} \right) \, dx \, dy \ne 0[/latex] for [latex] n=1,2,3,... [/latex] and [latex] m=1,2,3,... [/latex]

 

Thank you in advance...

Edited February 3, 2014 by eleteroboltz

[studiot]

What would your upper limits L and H be?

You know they are functions, not constants ?

[eleteroboltz]

L and H are constants, reals and greater than 0.

n and m are integers greater than 0.

Edited February 3, 2014 by eleteroboltz

[Endercreeper01]

Can [latex]b(x, y)[/latex] include 0?

If so, [latex]b(x,y)[/latex] can be [latex]0xy[/latex], or more generally, [latex]b(x,y)=0f(x,y)[/latex], where [latex]f(x,y)[/latex] is some other function of x an y.

Edited February 4, 2014 by Endercreeper01