s11aa returns the value of the inverse hyperbolic tangent, arctanh x
Syntax
| C# |
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public static double s11aa( double x, out int ifail ) |
| Visual Basic (Declaration) |
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Public Shared Function s11aa ( _ x As Double, _ <OutAttribute> ByRef ifail As Integer _ ) As Double |
| Visual C++ |
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public: static double s11aa( double x, [OutAttribute] int% ifail ) |
| F# |
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static member s11aa : x:float * ifail:int byref -> float |
Parameters
- x
- Type: System..::.Double
On entry: the argumentConstraint:
- ifail
- Type:
System..::.Int32
%
On exit:
Return Value
s11aa returns the value of the inverse hyperbolic tangent, arctanh x
Description
s11aa calculates an approximate value for the inverse hyperbolic tangent of its argument, arctanh x
For x 2 ≤ 1 2
where -
1 2 ≤ x ≤
1 2 , - 1 ≤ t ≤ 1 and t = 4 x 2 - 1
For 1 2 < x 2 < 1
For x ≥ 1 arctanh x
References
Error Indicators and Warnings
Errors or warnings detected by the method:
Accuracy
If δ ε
That is, the relative error in the argument, x
x 1 - x 2 arctanh x
in the result. The equality should hold if δ δ δ
The behaviour of the amplification factor is shown in the following graph:
Figure 1
The factor is not significantly greater than one except for arguments close to Further Comments
None.
Example
This example reads values of the argument x x
Example program (C#): s11aae.cs
