Power Series Expansion for Real Area Hyperbolic Cosecant

Theorem
The (real) area hyperbolic cosecant function has a Taylor series expansion:

Proof
From Power Series Expansion for Real Area Hyperbolic Sine:

From Real Area Hyperbolic Sine of Reciprocal equals Real Area Hyperbolic Cosecant:


 * $\map \arsinh {\dfrac 1 x} = \arcsch x$

So:

Hence the result.

Also see

 * Power Series Expansion for Real Inverse Hyperbolic Sine
 * Power Series Expansion for Real Inverse Hyperbolic Cosine
 * Power Series Expansion for Real Inverse Hyperbolic Tangent
 * Power Series Expansion for Real Inverse Hyperbolic Cotangent
 * Power Series Expansion for Real Inverse Hyperbolic Secant