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In the below snippet, the equations are listed that need to be used to solve for the Padé approximant. How are these equations derived? I get they want the derivatives to be equal at zero, but I don't see how those equations follow from that knowledge.

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saei
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  • What is the connection between the derivatives at zero of a power series and its coefficients? – Somos Mar 26 '20 at 11:30
  • How does that help? $R(x)$ is not a power series, it's a fraction of power series, so to get derivatives, I need quotient rule. – saei Mar 26 '20 at 11:37
  • Could you provide the source of the snippet? Pade approximation is defined by (3). It is not that obvious to me that it is should be equivalent to (5). BTW, b_0 can be set to 1 without loss of generality. – hans Mar 26 '24 at 09:15

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