Related Series
- There are seven related series of two variables, Φ1, Φ2, Φ3, Ψ1, Ψ2, Ξ1, and Ξ2, which generalize Kummer's confluent hypergeometric function 1F1 of one variable and the confluent hypergeometric limit function 0F1 of one variable in a similar manner. The first of these was introduced by Pierre Humbert in 1920.
- Giuseppe Lauricella (1893) defined four functions similar to the Appell series, but depending on many variables rather than just the two variables x and y. These series were also studied by Appell. They satisfy certain partial differential equations, and can also be given in terms of Euler-type integrals and contour integrals.
Read more about this topic: Appell Series
Famous quotes containing the words related and/or series:
“One does not realize the historical sensation as a re-experiencing, but as an understanding that is closely related to the understanding of music, or rather of the world by means of music.”
—Johan Huizinga (1872–1945)
“History is nothing but a procession of false Absolutes, a series of temples raised to pretexts, a degradation of the mind before the Improbable.”
—E.M. Cioran (b. 1911)