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generalized hypergeometric function 0F2

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1: 16.2 Definition and Analytic Properties
§16.2(i) Generalized Hypergeometric Series
Polynomials
Note also that any partial sum of the generalized hypergeometric series can be represented as a generalized hypergeometric function via …
§16.2(v) Behavior with Respect to Parameters
2: 35.8 Generalized Hypergeometric Functions of Matrix Argument
§35.8 Generalized Hypergeometric Functions of Matrix Argument
§35.8(i) Definition
Convergence Properties
§35.8(iv) General Properties
Confluence
3: 15.2 Definitions and Analytical Properties
§15.2(i) Gauss Series
In general, F ( a , b ; c ; z ) does not exist when c = 0 , - 1 , - 2 , . … …
§15.2(ii) Analytic Properties
The same properties hold for F ( a , b ; c ; z ) , except that as a function of c , F ( a , b ; c ; z ) in general has poles at c = 0 , - 1 , - 2 , . …
4: 17.1 Special Notation
§17.1 Special Notation
k , j , m , n , r , s nonnegative integers.
Another function notation used is the ‘‘idem’’ function: … Fine (1988) uses F ( a , b ; t : q ) for a particular specialization of a ϕ 1 2 function.
5: 8.19 Generalized Exponential Integral
§8.19 Generalized Exponential Integral
§8.19(i) Definition and Integral Representations
§8.19(ii) Graphics
§8.19(vi) Relation to Confluent Hypergeometric Function
§8.19(xi) Further Generalizations
6: 8.21 Generalized Sine and Cosine Integrals
§8.21 Generalized Sine and Cosine Integrals
§8.21(iii) Integral Representations
Spherical-Bessel-Function Expansions
§8.21(vii) Auxiliary Functions
§8.21(viii) Asymptotic Expansions
7: 35.7 Gaussian Hypergeometric Function of Matrix Argument
§35.7 Gaussian Hypergeometric Function of Matrix Argument
§35.7(i) Definition
Jacobi Form
Confluent Form
Integral Representation
8: 35.6 Confluent Hypergeometric Functions of Matrix Argument
§35.6 Confluent Hypergeometric Functions of Matrix Argument
§35.6(i) Definitions
Laguerre Form
§35.6(ii) Properties
§35.6(iv) Asymptotic Approximations
9: 19.16 Definitions
§19.16(ii) R - a ( b ; z )
All elliptic integrals of the form (19.2.3) and many multiple integrals, including (19.16.3), are special cases of a multivariate hypergeometric functionFor generalizations and further information, especially representation of the R -function as a Dirichlet average, see Carlson (1977b).
§19.16(iii) Various Cases of R - a ( b ; z )
10: 15.10 Hypergeometric Differential Equation
§15.10 Hypergeometric Differential Equation
15.10.1 z ( 1 - z ) d 2 w d z 2 + ( c - ( a + b + 1 ) z ) d w d z - a b w = 0 .
Singularity z = 0
Singularity z = 1
Singularity z =