special case
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1: 12.18 Methods of Computation
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►Because PCFs are special cases of confluent hypergeometric functions, the methods of computation described in §13.29 are applicable to PCFs.
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2: 17.16 Mathematical Applications
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►Many special cases of -series arise in the theory of partitions, a topic treated in §§27.14(i) and 26.9.
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3: 16.18 Special Cases
§16.18 Special Cases
►The and functions introduced in Chapters 13 and 15, as well as the more general functions introduced in the present chapter, are all special cases of the Meijer -function. …As a corollary, special cases of the and 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 -function. …4: 6.9 Continued Fraction
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6.9.1
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5: 12.20 Approximations
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►As special cases of these results a Chebyshev-series expansion for valid when follows from (12.7.14), and Chebyshev-series expansions for and valid when follow from (12.4.1), (12.4.2), (12.7.12), and (12.7.13).
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6: 31.12 Confluent Forms of Heun’s Equation
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►This has regular singularities at and , and an irregular singularity of rank 1 at .
►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.
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7: 30.2 Differential Equations
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§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
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►Cvijović and Klinowski (1994) contains fractional integrals (with free parameters) for and , together with special cases.
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10: 34.7 Basic Properties: Symbol
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