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21: 1.10 Functions of a Complex Variable
Picard’s Theorem
§1.10(iv) Residue Theorem
Rouché’s Theorem
Lagrange Inversion Theorem
Extended Inversion Theorem
22: 1.4 Calculus of One Variable
Mean Value Theorem
Fundamental Theorem of Calculus
First Mean Value Theorem
Second Mean Value Theorem
§1.4(vi) Taylor’s Theorem for Real Variables
23: 35.2 Laplace Transform
Convolution Theorem
24: 24.10 Arithmetic Properties
§24.10(i) Von Staudt–Clausen Theorem
25: 1.6 Vectors and Vector-Valued Functions
Green’s Theorem
Stokes’s Theorem
Gauss’s (or Divergence) Theorem
Green’s Theorem (for Volume)
26: 14.18 Sums
§14.18(i) Expansion Theorem
§14.18(ii) Addition Theorems
27: 23.20 Mathematical Applications
§23.20(ii) Elliptic Curves
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). … K always has the form T × r (Mordell’s Theorem: Silverman and Tate (1992, Chapter 3, §5)); the determination of r , the rank of K , raises questions of great difficulty, many of which are still open. …
28: 1.12 Continued Fractions
Pringsheim’s Theorem
Van Vleck’s Theorem
29: 18.2 General Orthogonal Polynomials
Markov’s theorem states that … Under further conditions on the weight function there is an equiconvergence theorem, see Szegő (1975, Theorem 13.1.2). … Part of this theorem was already proved by Blumenthal (1898). … See Szegő (1975, Theorem 7.2). …
30: 17.5 ϕ 0 0 , ϕ 0 1 , ϕ 1 1 Functions
q -Binomial Theorem