反三角函数、反双曲函数的单值解析分支

Single-valued Analytic Branch of Inverse Trigonometric Function and Inverse Hyperbolic Function

本文讨论了反三角函数Arcsinz=1iLn(iz+1-z2)、Arccosz=1iLn(z+i1-z2)、Arctanz=12iLn(1+i z1-i z)和反双曲函数Arsinhz=Ln(z+z2+1)、Arcoshz=Ln(z+z2-1)、Artanhz=12Ln1+z1-z的单值解析分支情况,并给出了其单值解析分支函数、支割线做法及应用.

This paper discussed the single-valued analytic branch for inverse trigonometric functions Arcsinz=1iLn（iz＋1-z2）、Arccosz=1iLn（z＋i1-z2）、Arctanz=12iLn（1＋i z1-i z）hyperbolic functions Asinhz=Ln（z＋z2＋1）、Arcoshz=Ln（z＋z2-1）、Artanhz=12Ln1＋z1-z ,its single-valued analytic branch function and secant approach and application were given.