Statements (52)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Special function
|
| gptkbp:citation |
gptkb:Abramowitz_and_Stegun,_Handbook_of_Mathematical_Functions
Gradshteyn and Ryzhik, Table of Integrals, Series, and Products |
| gptkbp:definedIn |
Hypergeometric series
|
| gptkbp:field |
gptkb:Mathematics
gptkb:Mathematical_analysis Complex analysis |
| gptkbp:generalizes |
Many elementary functions
|
| gptkbp:hasProperty |
Analytic continuation
Series expansion Symmetry properties Connection formulas Contiguous relations Integral representations Orthogonality (in special cases) Recurrence relations Transformation formulas |
| gptkbp:hasSpecialCase |
gptkb:Hermite_polynomial
gptkb:Chebyshev_polynomial gptkb:Exponential_function Bessel function Logarithm Legendre function Arcsin function Binomial series Elliptic integral Gegenbauer polynomial Jacobi polynomial |
| https://www.w3.org/2000/01/rdf-schema#label |
Hypergeometric function
|
| gptkbp:introduced |
gptkb:Carl_Friedrich_Gauss
|
| gptkbp:notation |
_2F_1
F(a,b;c;z) |
| gptkbp:parameter |
a
b c |
| gptkbp:relatedTo |
Appell function
Confluent hypergeometric function Generalized hypergeometric function Lauricella function |
| gptkbp:solution_of |
Hypergeometric differential equation
|
| gptkbp:used_in |
gptkb:Physics
gptkb:Number_theory gptkb:Probability_theory gptkb:Differential_equations gptkb:Quantum_mechanics Statistics Combinatorics |
| gptkbp:variant |
z
|
| gptkbp:bfsParent |
gptkb:Bessel_Polynomials
gptkb:Hypergeometric_distribution gptkb:Generalized_continued_fraction |
| gptkbp:bfsLayer |
8
|