Let 
be any function for which the integral
 |
converges. Then the expansion
![I(x)=(Gamma(p+1))/(x^(p+1))[A_0+(p+1)(A_1)/x+(p+1)(p+2)(A_2)/(x^2)+...],](/images/equations/BorelsExpansion/NumberedEquation2.svg) |
where 
is the gamma function, is usually an asymptotic
series for 
.
Borel's Expansion
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Cite this as:
Weisstein, Eric W. "Borel's Expansion." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BorelsExpansion.html