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Related

atanh-plot2d
plot2d(atanh(x),[x,-3,5]);

plot2d(atanh(x),[x,-3...

Calculate

atanh-load-solve-tanh

fb: .1;

t1: y[n] = tanh(x[n] ...

t2: solve(t1, y[n-1]);

Calculate

atanh-tanh

atanh (0.88);

Calculate

atanh-solve-tanh

fb: .1;

t1: y[n] = tanh(x[n] ...

t2: solve(t1, y[n]);

Calculate

atanh-diff

diff(atanh(x/2));

Calculate

atanh-integrate

integrate(atanh(x), x);

Calculate

atanh-solve-tanh

fb: .1;

t1: y[n] = tanh(x[n] ...

t2: solve(t1, y[n-1]);

Calculate

atanh

Run Example
(%i1)a:1;
(%o1)                                  1
(%i2) b:sqrt(2);
(%o2)                               sqrt(2)
(%i3) diff(asin(x),x) ;
                                      1
(%o3)                            ------------
                                           2
                                 sqrt(1 - x )
(%i4) diff(acos(x),x) ;
                                       1
(%o4)                           - ------------
                                            2
                                  sqrt(1 - x )
(%i5) diff(atan(x),x) ;
                                      1
(%o5)                               ------
                                     2
                                    x  + 1
(%i6) c:diff(asin(x)+acos(x),x);
(%o6)                                  0
(%i7) taylor(cos(x),x,0,5) ;
                                   2    4
                                  x    x
(%o7)/T/                      1 - -- + -- + . . .
                                  2    24
(%i8) taylor(log(1+x)/sin(x),x,0,5) ;
                            2    3       4        5
                       x   x    x    11 x    157 x
(%o8)/T/           1 - - + -- - -- + ----- - ------ + . . .
                       2   2    3     40      720
(%i9) taylor(atanh(x),x,0,4) ;
                                     3
                                    x
(%o9)/T/                        x + -- + . . .
                                    3
(%i10) limit((1+(1/n))^n,n,inf);
(%o10)                                %e
(%i11) 
Run Example
diff(atanh(x/2), x), ratsimp;
                                       2
(%o1)                              - ------
                                      2
                                     x  - 4
(%i2) 
Run Example
fb: .1;
(%o1)                                 0.1
(%i2) t1: y[n] = tanh(x[n] + y[n-1] * fb);
(%o2)                     y  = tanh(x  + 0.1 y     )
                           n         n        n - 1
(%i3) t2: solve(t1, y[n-1]);

rat: replaced 0.1 by 1/10 = 0.1
(%o3)                   [y      = 10 atanh(y ) - 10 x ]
                          n - 1             n        n
(%i4) t3: 10*atanh(y[n]) - 10*x[n];
(%o4)                        10 atanh(y ) - 10 x
                                       n        n
(%i5) solve(t2, y[n]);
                                           y
                                            n - 1
(%o5)                      [y  = tanh(x  + ------)]
                             n         n     10
(%i6) load(solve_rec);
(%o6)   /usr/share/maxima/5.21.1/share/contrib/solve_rec/solve_rec.mac
(%i7) solve_rec(t2, y[n-1]);
(%o7)                                false
(%i8) 

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