# Continued fraction of function (1) Calculator

## Calculates the continued fraction expansion of function f(x) with n terms. a0/(b0+a1/(b1+a2/(b2+...

 $\normal f(x)={\large\frac{a_0}{b_0+{\large\frac{a_1}{b_1+{\large\frac{a_2}{b_2+...}}}}}}\\$

 a0 the 1st term numerator b0 the 1st term denominator an the n-th term numerator bn the n-th term denominator x variable 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 $\normal Continued\ fraction\\\hspace{50} f(x)={\large\frac{a_0}{b_0+{\large\frac{a_1}{b_1+{\large\frac{a_2}{b_2+...}}}}}}\\[10](1)\ f(x)=\lim_{\small{n \to \infty}}f_n(x)\\\hspace{50}f_n(x)={\large\frac{a_0}{b_0+}\frac{a_1}{b_1+}\frac{a_2}{b_2+}\ \cdots\ \frac{a_n}{b_n+}}\\(2)\ Example\\[10] function\hspace{5} a_0\hspace{35} b_0\hspace{50} a_n\hspace{60} b_n\\[5] e^{x}-1\hspace{35} x\hspace{38} 1\hspace{45} -nx\hspace{30} x+n+1\\[10] tanx\hspace{35} x\hspace{38} 1\hspace{45} -x^2\hspace{42} 2n+1\\[10] tan^{\tiny{-1}}x\hspace{23} x\hspace{38} 1\hspace{45} (nx)^2\hspace{35}2n+1\\ erf(x)\hspace{7}{\large\frac{2x}{\sqrt\pi}}e^{\small{-x^2}}\hspace{18} 1\hspace{27} (-1)^{n}2nx^2\hspace{15}2n+1\\ erfc(x)\hspace{3}{\large\frac{2x}{\sqrt\pi}}e^{\small{-x^2}}\hspace{3} 1+2x^2\hspace{4} {\small-}2n(2n-1)\hspace{4}2x^2+4n+1\\$

Continued fraction of function (1)
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