### Abstract

It is shown that the Lauricella functions F_{D} in n variables transform as basis vectors corresponding to irreducible representations of the Lie algebra sl(n + 3, ℂ). Group representation theory can then be applied to derive addition theorems, transformation formulas, and generating functions for the F_{D}. It is clear from this analysis that the use of SL(m, ℍ) symmetry in atomic and elementary particle physics will lead inevitably to the remarkable functions F_{D}.

Original language | English (US) |
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Pages (from-to) | 1393-1399 |

Number of pages | 7 |

Journal | Journal of Mathematical Physics |

Volume | 13 |

Issue number | 9 |

DOIs | |

State | Published - Jan 1 1972 |

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## Cite this

Miller, W. (1972). Lie theory and the Lauricella functions F

_{D}.*Journal of Mathematical Physics*,*13*(9), 1393-1399. https://doi.org/10.1063/1.1666152