Opened 6 years ago

Closed 6 years ago

## #90 closed defect (fixed)

# (atanh -2)?

Reported by: | Raymond Toy | Owned by: | somebody |
---|---|---|---|

Priority: | major | Milestone: | |

Component: | Core | Version: | 2013-12 |

Keywords: | Cc: |

### Description

CMUCL 20e says `(atanh -2)`

is `#C(-0.54930615 -1.5707964)`

. This is consistent with what the CLHS says about `atanh`

for `x < -1`

being continuous with Quadrant III because `(atanh #c(-2.0 -0.0))`

is the same.

However, from the definition

atanh(z) = 1/2*(log(1+z) - log(1-z))

we have

atanh(-2) = 1/2*(log(-1) - log(3)) = 1/2*(i*pi - log(3)) = -log(3)/2 + i*pi/2

That is, the imaginary part should be positive. This would be consistent with the rule that atanh is continuous with Quadrant II.

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commit ca2bf8c29d22aaf44caf31f1d7b6ba77ab418be5 Author: Raymond Toy <toy.raymond@…> Date: Tue Dec 24 12:57:45 2013 -0800