generalized hypergeometric function 0F2

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1: 16.2 Definition and Analytic Properties
Polynomials
Note also that any partial sum of the generalized hypergeometric series can be represented as a generalized hypergeometric function via …
3: 15.2 Definitions and Analytical Properties
§15.2(i) Gauss Series
In general, $F\left(a,b;c;z\right)$ does not exist when $c=0,-1,-2,\dots$. … …
§15.2(ii) Analytic Properties
The same properties hold for $F\left(a,b;c;z\right)$, except that as a function of $c$, $F\left(a,b;c;z\right)$ in general has poles at $c=0,-1,-2,\dots$. …
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 ${{}_{2}\phi_{1}}$ function.
9: 19.16 Definitions
§19.16(ii) $R_{-a}\left(\mathbf{b};\mathbf{z}\right)$
All elliptic integrals of the form (19.2.3) and many multiple integrals, including (19.23.6) and (19.23.6_5), 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).