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1: 10.55 Continued Fractions
2: 4.30 Elementary Properties
3: 4.17 Special Values and Limits
4: 18.31 Bernstein–Szegő Polynomials
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►Let be a polynomial of degree and positive when .
The Bernstein–Szegő polynomials
, , are orthogonal on with respect to three types of weight function: , , .
In consequence, can be given explicitly in terms of and sines and cosines, provided that in the first case, in the second case, and in the third case.
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5: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
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►For , the multinomial coefficient is defined to be .
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is the multinominal coefficient (26.4.2):
… is the number of permutations of with cycles of length 1, cycles of length 2, , and cycles of length :
… is the number of set partitions of with subsets of size 1, subsets of size 2, , and subsets of size :
…For each all possible values of are covered.
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6: 34.5 Basic Properties: Symbol
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►If any lower argument in a symbol is , , or , then the symbol has a simple algebraic form.
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34.5.4
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34.5.11
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34.5.18
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34.5.22
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7: 24.20 Tables
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►Abramowitz and Stegun (1964, Chapter 23) includes exact values of , , ; , , , , 20D; , , 18D.
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►For information on tables published before 1961 see Fletcher et al. (1962, v. 1, §4) and Lebedev and Fedorova (1960, Chapters 11 and 14).