addition formulas

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1: 4.24 Inverse Trigonometric Functions: Further Properties

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§4.24(iii) Addition Formulas

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2: 4.35 Identities

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§4.35(i) Addition Formulas

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3: 4.38 Inverse Hyperbolic Functions: Further Properties

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§4.38(iii) Addition Formulas

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4: 21.6 Products

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§21.6(ii) Addition Formulas

… ►For addition formulas for classical theta functions see §20.7(ii).

5: 4.21 Identities

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§4.21(i) Addition Formulas

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6: 20.11 Generalizations and Analogs

… ►Such sets of twelve equations include derivatives, differential equations, bisection relations, duplication relations, addition formulas (including new ones for theta functions), and pseudo-addition formulas. …

7: 22.16 Related Functions

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Quasi-Addition and Quasi-Periodic Formulas

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Properties

► $\mathrm{Z}\left(x|k\right)$ satisfies the same quasi-addition formula as the function $ℰ(x,k)$, given by (22.16.27). …

8: 20.7 Identities

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§20.7(ii) Addition Formulas

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9: Bibliography K

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Jacobi polynomials. III. An analytic proof of the addition formula. SIAM. J. Math. Anal. 6, pp. 533–543.

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External Links:

Document, MathReview (G. Gasper), ZentralBlatt

Referenced by:

§18.18(ii).

Encodings:

BibTeX

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The addition formula for Laguerre polynomials. SIAM J. Math. Anal. 8 (3), pp. 535–540.

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External Links:

Document, MathReview (M. Mikolas), ZentralBlatt

Referenced by:

§18.14(i), §18.17(ii).

Encodings:

BibTeX

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10: 23.20 Mathematical Applications

… ►It follows from the addition formula (23.10.1) that the points $P_j=P(z_j)$, $j=1,2,3$, have zero sum iff $z_1+z_2+z_3\in 𝕃$, so that addition of points on the curve $C$ corresponds to addition of parameters $z_j$ on the torus $ℂ/𝕃$; see McKean and Moll (1999, §§2.11, 2.14). …