addition formula
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11: 25.16 Mathematical Applications
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25.16.12
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12: 19.26 Addition Theorems
§19.26 Addition Theorems
►§19.26(i) General Formulas
… ►§19.26(iii) Duplication Formulas
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19.26.27
, or .
13: 18.17 Integrals
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►For addition formulas corresponding to (18.17.5) and (18.17.6) see (18.18.8) and (18.18.9), respectively.
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14: 30.10 Series and Integrals
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►For product formulas and convolutions see Connett et al. (1993).
For an addition theorem, see Meixner and Schäfke (1954, p. 300) and King and Van Buren (1973).
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15: 18.3 Definitions
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3.
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►For representations of the polynomials in Table 18.3.1 by Rodrigues formulas, see §18.5(ii).
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►In this chapter, formulas for the Chebyshev polynomials of the second, third, and fourth kinds will not be given as extensively as those of the first kind.
However, most of these formulas can be obtained by specialization of formulas for Jacobi polynomials, via (18.7.4)–(18.7.6).
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►Formula (18.3.1) can be understood as a Gauss-Chebyshev quadrature, see (3.5.22), (3.5.23).
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As given by a Rodrigues formula (18.5.5).
16: 19.11 Addition Theorems
17: 3.3 Interpolation
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►Newton’s formula has the advantage of allowing easy updating: incorporation of a new point requires only addition of the term with to (3.3.38), plus the computation of this divided difference.
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18: 5.9 Integral Representations
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5.9.2_5
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Binet’s Formula
… ►Two alternative versions of Binet’s formula are ►
5.9.10_1
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5.9.10_2
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19: 18.18 Sums
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