# relations to confluent hypergeometric functions of matrix argument

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## 8 matching pages

##### 1: 35.6 Confluent Hypergeometric Functions of Matrix Argument

###### §35.6(iii) Relations to Bessel Functions of Matrix Argument

…##### 2: Software Index

*a*’ indicates available functionality through optional or add-on packages; an empty space indicates no known support. … ►In the list below we identify four main sources of software for computing special functions. … ►

These are collections of software (e.g. libraries) or interactive systems of a somewhat broad scope. Contents may be adapted from research software or may be contributed by project participants who donate their services to the project. The software is made freely available to the public, typically in source code form. While formal support of the collection may not be provided by its developers, within active projects there is often a core group who donate time to consider bug reports and make updates to the collection.

Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.

A cross index of mathematical software in use at NIST.

##### 3: 33.22 Particle Scattering and Atomic and Molecular Spectra

##### 4: Bibliography B

##### 5: Bibliography D

##### 6: Bibliography

##### 7: Bibliography M

##### 8: Errata

Originally the matrix in the argument of the Gaussian hypergeometric function of matrix argument ${}_{2}{}^{}F_{1}^{}$ was written with round brackets. This matrix has been rewritten with square brackets to be consistent with the rest of the DLMF.

A note about the multivalued nature of the Kummer confluent hypergeometric function of the second kind $U$ on the right-hand side of (7.18.10) was inserted.

The generalized hypergeometric function of matrix argument ${}_{p}{}^{}F_{q}^{}({a}_{1},\mathrm{\dots},{a}_{p};{b}_{1},\mathrm{\dots},{b}_{q};\mathbf{T})$, was linked inadvertently as its single variable counterpart ${}_{p}{}^{}F_{q}^{}({a}_{1},\mathrm{\dots},{a}_{p};{b}_{1},\mathrm{\dots},{b}_{q};\mathbf{T})$. Furthermore, the Jacobi function of matrix argument ${P}_{\nu}^{(\gamma ,\delta )}\left(\mathbf{T}\right)$, and the Laguerre function of matrix argument ${L}_{\nu}^{(\gamma )}\left(\mathbf{T}\right)$, were also linked inadvertently (and incorrectly) in terms of the single variable counterparts given by ${P}_{\nu}^{(\gamma ,\delta )}\left(\mathbf{T}\right)$, and ${L}_{\nu}^{(\gamma )}\left(\mathbf{T}\right)$. In order to resolve these inconsistencies, these functions now link correctly to their respective definitions.

Confluent hypergeometric functions were incorrectly linked to the definitions of the Kummer confluent hypergeometric and parabolic cylinder functions. However, to the eye, the functions appeared correct. The links were corrected.

A new Subsection Continued Fractions, has been added to cover computation of confluent hypergeometric functions by continued fractions.