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RC-function

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1: 19.2 Definitions
§19.2(iv) A Related Function: R C ( x , y )
Let x ( , 0 ) and y { 0 } . …Formulas involving Π ( ϕ , α 2 , k ) 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 ( x , y ) . … When x and y are positive, R C ( x , y ) 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 ( x , x ) and R C ( 0 , y ) see (19.6.15). …