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how to obtain the inverse series for multivariable functions using

  • To: mathgroup at smc.vnet.net
  • Subject: [mg130587] how to obtain the inverse series for multivariable functions using
  • From: Qi Hao <xqi.hao at gmail.com>
  • Date: Wed, 24 Apr 2013 07:02:54 -0400 (EDT)
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Hello, everyone:
 Now, I have a question about how to obtain the inverse series for multivariable functions. The system of nonlinear equations is like this:
x = f(p,q)
y = g(p,q).
The inverse functions are 
p = h(x,y)
q = r(x,y).
Now, I have known the taylor expansion of x and y with respect to p and q at point(0,0), that is
x = f(0,0) + df/dp(0,0)p + df/dq(0,0)q + ...
y = g(0,0) + dg/dp(0,0)p + dg/dq(0,0)q + ...
I want to know the taylor expansion of the inverse functions, that is
p = h(0,0) + dh/dx(0,0)x + dh/dx(0,0)y + ...
q = r(0,0) + dr/dx(0,0)x + dr/dy(0,0)y + ...

Could you show me your mathematica codes to solve this problem ?

Thank you very much!

Qi Hao



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