inverse series

31/03/2010 - 01:27 von Regina | Report spam
Hi there, i have a problem i simply cant solve: consider z->0, Q->inf
and z=Exp(-Q)(1+a1/Q+a2/Q^2+...)

I want an inverse series, something like Q=-log(z)+... how do i get
the next term in the expansion for Q?
thanks. alex
 

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#1 Arnold Neumaier
31/03/2010 - 13:36 | Warnen spam
Regina wrote:
Hi there, i have a problem i simply cant solve: consider z->0, Q->inf
and z=Exp(-Q)(1+a1/Q+a2/Q^2+...)

I want an inverse series, something like Q=-log(z)+... how do i get
the next term in the expansion for Q?



Take the logarithm on both sides and expand to get
log z = -Q + log(1+a1/Q+a2/Q^2+...)= -Q+a1/Q +b1/Q^2+,
hence
Q = -log z +a1/Q +b1/Q^2+
Now iterate in this equation, starting with Q_0=-log z

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