3 edition of Generalized Hypergeometric Equation found in the catalog.
Source title: Generalized Hypergeometric Equation: Transformations and Group Theoretical Aspects (IPH001)
|Statement||Iop Publishing Ltd|
|Publishers||Iop Publishing Ltd|
|LC Classifications||Dec 22, 2018|
|The Physical Object|
|Pagination||xvi, 135 p. :|
|Number of Pages||75|
nodata File Size: 4MB.
Hypergeometric and Legendre Functions with Applications to Integral Equations of Potential Theory. Generalized hypergeometric functions include the Gaussian and the as special cases, which in turn have many particular as special cases, such as, and the. Dougall's formula [ ] Dougall's formula gives the sum of a very series that is terminating and 2-balanced.
During the twentieth century this was a fruitful area of combinatorial mathematics, with numerous connections to other fields. This cancelling is a special case of a reduction formula that may be applied whenever a parameter on the top row differs from one on the bottom row by a non-negative integer. This is then a divergent or asymptotic series, or it can be interpreted as a symbolic shorthand for a differential equation that the sum satisfies Generalized Hypergeometric Equation. In tensor product decompositions of concrete representations of this group are met, which can be written as 3 F 2 hypergeometric series.
These are sometimes called Gauss's hypergeometric functions, classical standard hypergeometric or often simply hypergeometric functions. Generalizations [ ] The generalized hypergeometric function is linked to the and the. Cambridge, UK: Cambridge University Press. Encyclopedia of Mathematics and Its Applications. The series without the factor of n! Ina Generalized Hypergeometric Equation hypergeometric series is a in which the ratio of successive indexed by n is a of n.
An important generalization of Gosper's technique, calledin turn led to the powerful machinery of the Zeilberger 1990. Special cases [ ] Many of the special functions in mathematics are special cases of the or the ; see the corresponding articles for examples.
Special hypergeometric functions occur as on and semi-simple. 2013"Generalized hypergeometric functions: product identities and weighted norm inequalities", The Ramanujan Journal, 31 1—2 : 53—66, :,• Commentationes Societatis Regiae Scientarum Gottingensis Recentiores in Latin. The last fifteen were given by Gauss in his 1812 paper. Olde 2010, in ; Lozier, Daniel M. This function was first studied in detail bywho explored the conditions for its convergence. Also, if any of the parameters a j is equal to any of the parameters b k, then the matching parameters can be "cancelled out", with certain exceptions when the parameters are non-positive integers.
are a generalization of generalized hypergeometric functions where the Pochhammer symbols in the series expression are generalised to gamma functions of linear expressions in the index n. 1 The factor of in the is present for historical reasons of notation.
60 in Washington, DC: Hemisphere, pp.
Generalizations [ ] The generalized hypergeometric function is linked to the and the.
A generalization, the analogues, called the , were given by in the late nineteenth century.