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## Main Question or Discussion Point

Hi. I have been experimenting a little to come up with the following "conjecture"

[tex]

\int_0^{2\pi}d\phi f(a+b\cos\phi)\sin\phi=0

[/tex]

where a and b are arbitrary constants and f(x) is any function. Is this true? I guess it can be shown by expanding f in a power series of cosines?

[tex]

\int_0^{2\pi}d\phi f(a+b\cos\phi)\sin\phi=0

[/tex]

where a and b are arbitrary constants and f(x) is any function. Is this true? I guess it can be shown by expanding f in a power series of cosines?