# special cases

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##### 1: 12.18 Methods of Computation
Because PCFs are special cases of confluent hypergeometric functions, the methods of computation described in §13.29 are applicable to PCFs. …
##### 2: 17.16 Mathematical Applications
Many special cases of $q$-series arise in the theory of partitions, a topic treated in §§27.14(i) and 26.9. …
##### 3: 16.18 Special Cases
###### §16.18 SpecialCases
The ${{}_{1}F_{1}}$ and ${{}_{2}F_{1}}$ functions introduced in Chapters 13 and 15, as well as the more general ${{}_{p}F_{q}}$ functions introduced in the present chapter, are all special cases of the Meijer $G$-function. …As a corollary, special cases of the ${{}_{1}F_{1}}$ and ${{}_{2}F_{1}}$ functions, including Airy functions, Bessel functions, parabolic cylinder functions, Ferrers functions, associated Legendre functions, and many orthogonal polynomials, are all special cases of the Meijer $G$-function. …
##### 4: 6.9 Continued Fraction
6.9.1 $E_{1}\left(z\right)=\cfrac{e^{-z}}{z+\cfrac{1}{1+\cfrac{1}{z+\cfrac{2}{1+% \cfrac{2}{z+\cfrac{3}{1+\cfrac{3}{z+}}}}}}}\cdots,$ $|\operatorname{ph}z|<\pi$.
##### 5: 12.20 Approximations
As special cases of these results a Chebyshev-series expansion for $U\left(a,x\right)$ valid when $\lambda\leq x<\infty$ follows from (12.7.14), and Chebyshev-series expansions for $U\left(a,x\right)$ and $V\left(a,x\right)$ valid when $0\leq x\leq\lambda$ follow from (12.4.1), (12.4.2), (12.7.12), and (12.7.13). …
##### 6: 31.12 Confluent Forms of Heun’s Equation
This has regular singularities at $z=0$ and $1$, and an irregular singularity of rank 1 at $z=\infty$. Mathieu functions (Chapter 28), spheroidal wave functions (Chapter 30), and Coulomb spheroidal functions (§30.12) are special cases of solutions of the confluent Heun equation. …
##### 9: 19.13 Integrals of Elliptic Integrals
Cvijović and Klinowski (1994) contains fractional integrals (with free parameters) for $F\left(\phi,k\right)$ and $E\left(\phi,k\right)$, together with special cases. …