Solving Tanh[x]=Tanh[a]Tanh[b x + c]

Discussion in 'Mathematica' started by Yaroslav Bulatov, Nov 20, 2007.

  1. I'd like to use Mathematica to show that solution of Tanh[x] - Tanh[a]
    Tanh[b x + c]=0 can be written as
    1/2 Log (Root[c1 x^(1+b) + c2 x^b + c3 x -1]) for certain coefficients
    c1,c2,c3 when b is a positive integer

    Tanh[x] - Tanh[a] Tanh[b x + c]// TrigToExp // Together // Numerator
    gives me almost what I need, except now I need to factor out Exp[2x]
    as a separate variable. What's the best way of achieving it? Using
    syntactic replacement rules like {Exp[a_+b_]->Exp[a]Exp,Exp[2x]->x}
    seems like an uphill battle against the evaluator which automatically
    simplifies Exp expressions

    Yaroslav Bulatov, Nov 20, 2007
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  2. Yaroslav Bulatov

    dh Guest

    Hi Yaroslav,

    you must prevent the "uphill battle" by e.g. temporarily write

    Exp[a]Exp as {Exp[a],Exp}, then do what you want and finally

    eliminate the braces.E.g:

    .... //.{Exp[a__+b_]->{Exp[a],Exp},Exp[2x]->x,{a_,b_}->a b}

    hope this helps, Daniel

    dh, Nov 22, 2007
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