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1: 34.2 Definition: Symbol
§34.2 Definition: Symbol
►The quantities in the symbol are called angular momenta. …They therefore satisfy the triangle conditions …where is any permutation of . The corresponding projective quantum numbers are given by …2: Simon Ruijsenaars
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► 1948 in Hillegom, The Netherlands) is a Professor of Mathematical Physics at the University of Leeds.
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3: 28 Mathieu Functions and Hill’s Equation
Chapter 28 Mathieu Functions and Hill’s Equation
…4: 31.18 Methods of Computation
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►Subsequently, the coefficients in the necessary connection formulas can be calculated numerically by matching the values of solutions and their derivatives at suitably chosen values of ; see Laĭ (1994) and Lay et al. (1998).
Care needs to be taken to choose integration paths in such a way that the wanted solution is growing in magnitude along the path at least as rapidly as all other solutions (§3.7(ii)).
The computation of the accessory parameter for the Heun functions is carried out via the continued-fraction equations (31.4.2) and (31.11.13) in the same way as for the Mathieu, Lamé, and spheroidal wave functions in Chapters 28–30.
5: Staff
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Ronald F. Boisvert, Editor at Large, NIST
Gerhard Wolf, University of Duisberg-Essen, Chap. 28
Diego Dominici, State University of New York at New Paltz, for Chaps. 9, 10 (deceased)
Amparo Gil, Universidad de Cantabria, for Chap. 3
Simon Ruijsenaars, University of Leeds, for Chaps. 5, 28
6: 26.3 Lattice Paths: Binomial Coefficients
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Table 26.3.2: Binomial coefficients for lattice paths.
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2 | 1 | 3 | 6 | 10 | 15 | 21 | 28 | 36 | 45 |
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6 | 1 | 7 | 28 | 84 | 210 | 462 | 924 | 1716 | 3003 |
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26.3.11
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7: 26.9 Integer Partitions: Restricted Number and Part Size
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denotes the number of partitions of into at most parts.
See Table 26.9.1.
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►Conjugation establishes a one-to-one correspondence between partitions of into at most parts and partitions of into parts with largest part less than or equal to .
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is the number of partitions of into at most parts, each less than or equal to .
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8: Gerhard Wolf
9: Bibliography Y
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On rational solutions of the second Painlevé equation.
Vesti Akad. Navuk. BSSR Ser. Fiz. Tkh. Nauk. 3, pp. 30–35 (Russian).
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Simple Variational Proof That Any Two-Dimensional Potential Well Supports at Least One Bound State.
American Journal of Physics 57 (1), pp. 85–86.
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Computation of the derivatives of the Riemann zeta-function in the complex domain.
USSR Comput. Math. and Math. Phys. 28 (4), pp. 115–124.
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10: 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
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►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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►This has irregular singularities at
and , each of rank .
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►This has a regular singularity at
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of rank .
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►This has one singularity, an irregular singularity of rank
at
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