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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 Special Cases
The F 1 1 and F 1 2 functions introduced in Chapters 13 and 15, as well as the more general F q p functions introduced in the present chapter, are all special cases of the Meijer G -function. …As a corollary, special cases of the F 1 1 and F 1 2 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 ( z ) = e - z z + 1 1 + 1 z + 2 1 + 2 z + 3 1 + 3 z + , | ph z | < π .
5: 12.20 Approximations
As special cases of these results a Chebyshev-series expansion for U ( a , x ) valid when λ x < follows from (12.7.14), and Chebyshev-series expansions for U ( a , x ) and V ( a , x ) valid when 0 x λ 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 = . 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. …
7: 30.2 Differential Equations
§30.2(iii) Special Cases
8: 29.5 Special Cases and Limiting Forms
§29.5 Special Cases and Limiting Forms
9: 19.13 Integrals of Elliptic Integrals
Cvijović and Klinowski (1994) contains fractional integrals (with free parameters) for F ( ϕ , k ) and E ( ϕ , k ) , together with special cases. …
10: 34.7 Basic Properties: 9 j Symbol
§34.7(i) Special Case