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Question Number 10563 by FilupS last updated on 18/Feb/17

can someone explain to me  big K notation? (I don′t know the name)  It is related to continuous fractions.  e.g.   x=b_0 +K_(i=1) ^∞ (a_i /b_i )     e^x =(x^0 /(0!))+(x^1 /(1!))+(x^2 /(2!))+...  e^x =Σ_(i=0) ^∞ (x^i /(i!))       =1+(x/(1−((1x)/(2+x−((2x)/(3+x−((3x)/(...))))))))  How do you interperate this in  big K notation?

$$\mathrm{can}\:\mathrm{someone}\:\mathrm{explain}\:\mathrm{to}\:\mathrm{me} \\ $$$$\mathrm{big}\:\mathrm{K}\:\mathrm{notation}?\:\left(\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{the}\:\mathrm{name}\right) \\ $$$$\mathrm{It}\:\mathrm{is}\:\mathrm{related}\:\mathrm{to}\:\mathrm{continuous}\:\mathrm{fractions}. \\ $$$$\mathrm{e}.\mathrm{g}.\:\:\:{x}={b}_{\mathrm{0}} +\underset{{i}=\mathrm{1}} {\overset{\infty} {\boldsymbol{\mathrm{K}}}}\frac{{a}_{{i}} }{{b}_{{i}} } \\ $$$$\: \\ $$$${e}^{{x}} =\frac{{x}^{\mathrm{0}} }{\mathrm{0}!}+\frac{{x}^{\mathrm{1}} }{\mathrm{1}!}+\frac{{x}^{\mathrm{2}} }{\mathrm{2}!}+... \\ $$$${e}^{{x}} =\underset{{i}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{{i}} }{{i}!} \\ $$$$\:\:\:\:\:=\mathrm{1}+\frac{{x}}{\mathrm{1}−\frac{\mathrm{1}{x}}{\mathrm{2}+{x}−\frac{\mathrm{2}{x}}{\mathrm{3}+{x}−\frac{\mathrm{3}{x}}{...}}}} \\ $$$$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{interperate}\:\mathrm{this}\:\mathrm{in} \\ $$$$\mathrm{big}\:\mathrm{K}\:\mathrm{notation}? \\ $$

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