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21: 23.20 Mathematical Applications
The geometric nature of this construction is illustrated in McKean and Moll (1999, §2.14), Koblitz (1993, §§6, 7), and Silverman and Tate (1992, Chapter 1, §§3, 4): each of these references makes a connection with the addition theorem (23.10.1). …
22: Bibliography C
  • B. C. Carlson (1971) New proof of the addition theorem for Gegenbauer polynomials. SIAM J. Math. Anal. 2, pp. 347–351.
  • H. S. Cohl (2013a) Fourier, Gegenbauer and Jacobi expansions for a power-law fundamental solution of the polyharmonic equation and polyspherical addition theorems. SIGMA Symmetry Integrability Geom. Methods Appl. 9, pp. Paper 042, 26.
  • 23: Bibliography D
  • S. C. Dhar (1940) Note on the addition theorem of parabolic cylinder functions. J. Indian Math. Soc. (N. S.) 4, pp. 29–30.
  • 24: Bibliography K
  • B. J. King and A. L. Van Buren (1973) A general addition theorem for spheroidal wave functions. SIAM J. Math. Anal. 4 (1), pp. 149–160.
  • 25: 21.7 Riemann Surfaces
    Fay derives (21.7.10) as a special case of a more general class of addition theorems for Riemann theta functions on Riemann surfaces. …
    26: 19.36 Methods of Computation
    When the values of complete integrals are known, addition theorems with ψ = π / 2 19.11(ii)) ease the computation of functions such as F ( ϕ , k ) when 1 2 π - ϕ is small and positive. …
    27: Tom M. Apostol
    In 1998, the Mathematical Association of America (MAA) awarded him the annual Trevor Evans Award, presented to authors of an exceptional article that is accessible to undergraduates, for his piece entitled “What Is the Most Surprising Result in Mathematics?” (Answer: the prime number theorem). …In addition, he was the co-author of New Horizons in Geometry, published by the MAA, which received the CHOICE “Outstanding Academic Title” award in 2013. …He additionally served as a visiting lecturer for the MAA, and as a member of the MAA Board of Governors. …
    28: 15.2 Definitions and Analytical Properties
    29: 1.10 Functions of a Complex Variable
    Picard’s Theorem
    §1.10(iv) Residue Theorem
    In addition, …
    Rouché’s Theorem
    Lagrange Inversion Theorem
    30: 1.12 Continued Fractions
    Pringsheim’s Theorem
    Van Vleck’s Theorem
    The continued fraction converges iff, in addition, …