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Added the word "satisfying"
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Andrew
Andrew
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Given a generating function $A(x)$, are there any general techniques for finding the asymptotics of the associated sequence? For example, given the generating function satisfying $A(x) = 1 + x\cdot A\left(\frac{x}{A(-x)}\right)$, is there anything we can say about how fast the coefficients grow?

Given a generating function $A(x)$, are there any general techniques for finding the asymptotics of the associated sequence? For example, given the generating function $A(x) = 1 + x\cdot A\left(\frac{x}{A(-x)}\right)$, is there anything we can say about how fast the coefficients grow?

Given a generating function $A(x)$, are there any general techniques for finding the asymptotics of the associated sequence? For example, given the generating function satisfying $A(x) = 1 + x\cdot A\left(\frac{x}{A(-x)}\right)$, is there anything we can say about how fast the coefficients grow?

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Andrew
Andrew
  • 111
  • 2

Asymptotics of Generating Functions

Given a generating function $A(x)$, are there any general techniques for finding the asymptotics of the associated sequence? For example, given the generating function $A(x) = 1 + x\cdot A\left(\frac{x}{A(-x)}\right)$, is there anything we can say about how fast the coefficients grow?