[math-fun] continued fractions

19 Oct 2017

      hello,

just to leave some formulas.

Formula 26

a := 
(sqrt(exp(2*Pi)-exp(Pi)+1)*sqrt(exp(2*Pi)+exp(Pi)+1)*sqrt(exp(8*Pi)+exp(2*Pi)+1)*sqrt(exp(12*Pi)+exp(10*Pi)+exp(8*Pi)+exp(6*Pi)+2*exp(4*Pi)-2*exp(2*Pi)+1))/(sqrt(5)*exp(4*Pi)+sqrt(5)*exp(2*Pi)+sqrt(5));

b:= 
-(a/2)+(exp(12*Pi)+exp(10*Pi)+exp(8*Pi)+exp(6*Pi)-1)/(2*(exp(4*Pi)+exp(2*Pi)+1));

phi:=a/(b+1/(1+exp(-2*Pi)/(1+exp(-4*Pi)/(1+exp(-6*Pi)/(1+exp(-8*Pi)/(1+exp(-2*Pi)/(1+exp(-4*Pi)/(1+exp(-6*Pi)/(1+exp(-8*Pi)/(1+ 
exp(-2*Pi)/(1+exp(-4*Pi)/(1+exp(-6*Pi)/(1+exp(-8*Pi)/(1+…))))))))))))));

Formula 27

a:=(sqrt(exp(2*Pi)+exp(Pi)+1)*sqrt(exp(3*Pi)+exp(2*Pi)+1)*sqrt(exp(5*Pi)-exp(4*Pi)+exp(2*Pi)-exp(Pi)+1)*sqrt(exp(10*Pi)+exp(9*Pi)+exp(7*Pi)+exp(5*Pi)+exp(4*Pi)+exp(3*Pi)-2*exp(2*Pi)+1))/(sqrt(5)*exp(3*Pi)+sqrt(5)*exp(2*Pi)+sqrt(5));

b:= -(a/2)+(exp(10*Pi)+exp(9*Pi)+exp(7*Pi)+exp(5*Pi)+ 
exp(4*Pi)-exp(3*Pi)-1)/(2*(exp(3*Pi)+exp(2*Pi)+1));

phi:=a/(b+1/(1+exp(-Pi)/(1+exp(-3*Pi)/(1+exp(-5*Pi)/(1+exp(-7*Pi)/(1+exp(-Pi)/(1+exp(-3*Pi)/(1+exp(-5*Pi)/(1+exp(-7*Pi)/(1+ 
exp(-Pi)/(1+exp(-3*Pi)/(1+exp(-5*Pi)/(1+exp(-7*Pi)/(1+…))))))))))))));

Formula 28

a:=(sqrt(24*exp(6*Pi)+12*exp(5*Pi)+4*exp(4*Pi)+2*exp(3*Pi)+7*exp(2*Pi)-2*exp(Pi)+1)*sqrt(24*exp(6*Pi)+12*exp(5*Pi)+4*exp 
(4*Pi)+2*exp(3*Pi)+7*exp(2*Pi)+2*exp(Pi)+1))/(6*sqrt(5)*exp(2*Pi)+3*sqrt(5)*exp(Pi)+sqrt(5)) 
;

b:= -(a/2)+ 
(24*exp(6*Pi)+12*exp(5*Pi)+4*exp(4*Pi)+2*exp(3*Pi)-5*exp(2*Pi)-1)/(2*(6*exp(2*Pi)+3*exp(Pi)+1));

phi:=a/(b+1/(1+exp(-Pi)/(2+exp(-2*Pi)/(3+exp(-3*Pi)/(4+exp(-4*Pi)/(1+exp(-Pi)/(2+exp(-2*Pi)/(3+exp(-3*Pi)/(4+exp(-4*Pi)/(1+ 
exp(-Pi)/(2+exp(-2*Pi)/(3+exp(-3*Pi)/(4+exp(-4*Pi)/(1+…))))))))))))));

Best regards

François...

François Mendzina Essomba

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