RC-function

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1: 19.2 Definitions

… ►

§19.2(iv) A Related Function: $R_{C}\left(x,y\right)$

►Let

x\in\mathbb{C}\setminus(-\infty,0)

and

y\in\mathbb{C}\setminus\{0\}

. …Formulas involving

\Pi\left(\phi,\alpha^{2},k\right)

that are customarily different for circular cases, ordinary hyperbolic cases, and (hyperbolic) Cauchy principal values, are united in a single formula by using

R_{C}\left(x,y\right)

. … ►When

x

and

y

are positive,

R_{C}\left(x,y\right)

is an inverse circular function if

x<y

and an inverse hyperbolic function (or logarithm) if

x>y

: …For the special cases of

R_{C}\left(x,x\right)

and

R_{C}\left(0,y\right)

see (19.6.15). …

RC-function

One matching page

1: 19.2 Definitions

§19.2(iv) A Related Function: R C ⁡ ( x , y )

§19.2(iv) A Related Function: $R_{C}\left(x,y\right)$