# Computation of the Complex Probability Function

## Abstract

The complex probability function is important in many areas of physics and many techniques have been developed in an attempt to compute it for some z quickly and e ciently. Most prominent are the methods that use Gauss-Hermite quadrature, which uses the roots of the n ^{th} degree Hermite polynomial and corresponding weights to approximate the complex probability function. This document serves as an overview and discussion of the use, shortcomings, and potential improvements on the Gauss-Hermite quadrature for the complex probability function.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1375900

- Report Number(s):
- LA-UR-17-27554

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Complex Probability Function Gauss Hermite Quadrature

### Citation Formats

```
Trainer, Amelia Jo, and Ledwith, Patrick John.
```*Computation of the Complex Probability Function*. United States: N. p., 2017.
Web. doi:10.2172/1375900.

```
Trainer, Amelia Jo, & Ledwith, Patrick John.
```*Computation of the Complex Probability Function*. United States. doi:10.2172/1375900.

```
Trainer, Amelia Jo, and Ledwith, Patrick John. Tue .
"Computation of the Complex Probability Function". United States.
doi:10.2172/1375900. https://www.osti.gov/servlets/purl/1375900.
```

```
@article{osti_1375900,
```

title = {Computation of the Complex Probability Function},

author = {Trainer, Amelia Jo and Ledwith, Patrick John},

abstractNote = {The complex probability function is important in many areas of physics and many techniques have been developed in an attempt to compute it for some z quickly and e ciently. Most prominent are the methods that use Gauss-Hermite quadrature, which uses the roots of the nth degree Hermite polynomial and corresponding weights to approximate the complex probability function. This document serves as an overview and discussion of the use, shortcomings, and potential improvements on the Gauss-Hermite quadrature for the complex probability function.},

doi = {10.2172/1375900},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Tue Aug 22 00:00:00 EDT 2017},

month = {Tue Aug 22 00:00:00 EDT 2017}

}

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