AngouriMath
SolveAHalfOddPowerOfOnePlusAnImaginaryHyperbolicSine(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
Half-odd powers of a ± i a sinh(y) beside anything in the hyperbolic functions of
y , by the half angle at which they are squares: 1 + i sinh(y) is
(cosh(y/2) + i sinh(y/2))^2 , so sqrt(a + i a sinh(y)) is
sqrt(a) (cosh(y/2) + i sinh(y/2)) times a constant on every interval where both
are continuous. The rest of the integrand is written in the half angle, and the question
asked again inx .
are continuous. The rest of the integrand is written in the half angle, and the question
asked again in
Remarks
were declined or searches past the budget: the half angle of
SolveByTheHalfAngleWhereOnePlusAHyperbolicCosineIsASquare(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean) reads
than of a real one.
times each power as written over the form it was rewritten to, a quotient whose
logarithmic derivative is zero, so it is constant wherever it is continuous and the
answer holds on every such interval, whatever
https://github.com/asc-community/AngouriMath/issues/718
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