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APEXCalculus / APEXCalculusV5

Tracks the current state of APEX Calculus. For the stable version that matches the latest print version, visit the repo APEXCalculusV4.
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csch inverse in terms of logarithms #11

Closed teepeemm closed 1 year ago

teepeemm commented 1 year ago

https://github.com/APEXCalculus/APEXCalculusV5/blob/2ec7e64191dfabbf1497bc7a00d3e2989614303b/text/06_Hyperbolic_Functions.tex#L346

"Logarithmic definitions of Inverse Hyperbolic Functions" and "Integrals Involving Inverse Hyperbolic Functions" both show how to define $\csch^{-1}x$ in terms of $\ln$. But they disagree by a negative sign when $x<0$. "Definitions" seems correct, not "Integrals". Playing around with Desmos, that negative sign can go in several different places: https://www.desmos.com/geometry-beta/8dnclvtqdt

Unfortunately, I've not thought of a nice way of combining the two fractions from "Definitions" without introducing the sgn function.

teepeemm commented 1 year ago

Never mind. I was overlooking the absolute value in "Integrals".