s18ce returns a value of the scaled modified Bessel function ${e}^{-\left|x\right|}{I}_{0}\left(x\right)$.

# Syntax

C# |
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public static double s18ce( double x ) |

Visual Basic |
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Public Shared Function s18ce ( _ x As Double _ ) As Double |

Visual C++ |
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public: static double s18ce( double x ) |

F# |
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static member s18ce : x : float -> float |

#### Parameters

- x
- Type: System..::..Double
*On entry*: the argument $x$ of the function.

#### Return Value

s18ce returns a value of the scaled modified Bessel function ${e}^{-\left|x\right|}{I}_{0}\left(x\right)$.

# Description

s18ce evaluates an approximation to ${e}^{-\left|x\right|}{I}_{0}\left(x\right)$, where ${I}_{0}$ is a modified Bessel function of the first kind. The scaling factor ${e}^{-\left|x\right|}$ removes most of the variation in ${I}_{0}\left(x\right)$.

The method uses the same Chebyshev expansions as s18ae, which returns the unscaled value of ${I}_{0}\left(x\right)$.

# References

Abramowitz M and Stegun I A (1972)

*Handbook of Mathematical Functions*(3rd Edition) Dover Publications# Error Indicators and Warnings

There are no actual failure exits from this method.

**_ifail**is always set to zero. This parameter is included for compatibility with other methods in this chapter.# Accuracy

Relative errors in the argument are attenuated when propagated into the function value. When the accuracy of the argument is essentially limited by the machine precision, the accuracy of the function value will be similarly limited by at most a small multiple of the machine precision.

# Parallelism and Performance

None.

# Further Comments

None.

# Example

This example reads values of the argument $x$ from a file, evaluates the function at each value of $x$ and prints the results.

Example program (C#): s18cee.cs