AngouriMath
SolveAnExponentialOfAHyperbolicFunctionBesideItsDerivative(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
An exponential of a multiple of a hyperbolic sine or cosine of a linear, beside a function
of the exponentials of the linear whose quotient by the derivative of that sine or cosine
is a rational function of it: underu = e^L + s e^(-L) , twice the cosine or the
sine,e^(n sinh(L)) cosh(L) is e^(n u/2)/2 , e^(n cosh(L)) tanh(L) is
e^(n u/2)/u , onto the exponential integral, and e^(n sinh(L)) sinh(2L) is
u e^(n u/2)/2 . The substitution answers the trigonometric ones written as nodes --
e^(n cos(x)) tan(x) is -Ei(n cos(x)) -- while a hyperbolic function arrives as
exponentials, and no rule read the sine or cosine in them. Rubi's 6.7.1.
https://github.com/asc-community/AngouriMath/issues/718
of the exponentials of the linear whose quotient by the derivative of that sine or cosine
is a rational function of it: under
sine,
exponentials, and no rule read the sine or cosine in them. Rubi's 6.7.1.
https://github.com/asc-community/AngouriMath/issues/718
Remarks
Every exponential of the variable but the outer one is a whole power of w = e^L , with
L the linear their exponents are whole multiples of, compared as polynomials and not
as written; the quotient is written inu = w + s/w by undetermined coefficients and a
check at points, or the rule declines.
as written; the quotient is written in
check at points, or the rule declines.
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