Funzioni di Lauricella

In matematica per serie ipergeometriche di Lauricella o funzioni di Lauricella si intendono quattro serie ipergeometriche di tre variabili introdotte e studiate da Giuseppe Lauricella nel 1893.

Definizioni

dove denota il simbolo di Pochhammer, cioè

Lauricella ha anche indicato l'esistenza di altre dieci interessanti funzioni ipergeometriche di tre variabili. Queste sono state individuate e studiate da Saran nel 1954. Si parla anche delle 14 funzioni ipergeometriche di Lauricella-Saran.

Generalizzazioni

Le quattro serie introdotte da Lauricella si possono estendere direttamente ad altrettante funzioni di variabili come segue.

Talora il termini serie ipergeometriche di Lauricella denota queste stesse serie.

Riduzioni

Quando si riducono le variabili a due si ottengono le serie ipergeometriche di Appell come segue:

Se ci si riduce ad una variabile tutte le quattro funzioni si riducono alla serie ipergeometrica di Gauss

Queste definizioni sono generalizzazioni della definizione della serie ipergeometrica.

Bibliografia

Collegamenti esterni

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