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Expand a function into a Thiele continued fraction
ResourceFunction["ThieleExpansion"][f,{x,x0,n}] generates a Thiele continued fraction expansion for f about the point x=x0 up to the nth order convergent, where n is an explicit integer. |
Compute the Thiele continued fraction for the exponential function around x=0:
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Thiele continued fraction of an arbitrary function around x=a:
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Use different methods for generating the Thiele expansion:
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The two methods will give results that are mathematically equivalent but may differ in form:
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Plot successive Thiele continued fraction approximations to exp(x):
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The Thiele expansion of order n is equivalent to the result of PadeApproximant of order {Ceiling[n/2],Floor[n/2]}:
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Thiele expansion is not defined for even or odd functions:
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Transform the variable to get a continued fraction expansion:
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