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Continued fraction of function (2)

Calculates the continued fraction expansion of function f(x) with n terms. b0+a1/(b1+a2/(b2+...

$\normal f(x)=b_0+{\large\frac{a_1}{b_1+{\large\frac{a_2}{b_2+...}}}}\\$

b₀

the 1st term

a_n

the n-th term numerator

b_n

the n-th term denominator

variable

n	fn(x)

$\normal Continued\ fraction\\ \hspace{50} f(x)=b_0+{\large\frac{a_1}{b_1+{\large\frac{a_2}{b_2+...}}}}\\[10] (1)\ f(x)=\lim_{\small{n \to \infty}}f_n(x)\\ \hspace{50}f_n(x)=b_0+{\large\frac{a_1}{b_1+}\frac{a_2}{b_2+}\ \cdots\ \frac{a_n}{b_n+}}\\[10] (2)\ Example\\[10] \hspace{20pt} function\hspace{10pt} b_0\hspace{30pt} a_n\hspace{25pt} b_n\\ \hspace{35pt} {\large\sqrt{x}} \hspace{48pt} 1\hspace{25pt} x-1\hspace{20pt} 2\\ \hspace{35pt} {\large\frac{x}{e^x-1}} \hspace{20pt} 1-{\large\frac{x}{2}}\hspace{20pt} {\large\frac{x^2}{4}}\hspace{20pt} 2n+1\\$

Continued fraction of function (2)

Calculates the continued fraction expansion of function f(x) with n terms. b0+a1/(b1+a2/(b2+...

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