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        general >> complex analysis >> Weirstrass Elliptic Function
        
(Message started by: Jason on Apr 10^th, 2004, 6:56pm)

Title: Weirstrass Elliptic Function
Post by Jason on Apr 10^th, 2004, 6:56pm

Let w₁=[alpha] and w₃=i[beta] for [alpha],[beta][in]R⁺. Show that P(u)[in]R for both Re(u)[in]{0,[alpha]} and Im(u)[in]{0,[beta]}

Title: Re: Weirstrass Elliptic Function
Post by Icarus on Apr 11^th, 2004, 6:34pm

I believe that follows from the formula

[smiley=frakcp.gif](z) = z^-2 + [sum]_[omega] ( (z-[omega])^-2 - [omega]^-2 ).

Where the sum is over all non-zero [omega] = n[omega]₁ + m[omega]₂, n, m [in] [bbz].

(All those symbols, and I still couldn't find the right "P" for the Weierstrauss function.)