q-binomial%20theorem
(0.002 seconds)
11—20 of 200 matching pages
11: Peter L. Walker
…
►Walker’s books are An Introduction to Complex Analysis, published by Hilger in 1974, The Theory of Fourier Series and Integrals, published by Wiley in 1986, Elliptic Functions. A Constructive Approach, published by Wiley in 1996, and Examples and Theorems in Analysis, published by Springer in 2004.
…
►
…
12: 27.2 Functions
…
►
§27.2(i) Definitions
… ►Euclid’s Elements (Euclid (1908, Book IX, Proposition 20)) gives an elegant proof that there are infinitely many primes. … ►(See Gauss (1863, Band II, pp. 437–477) and Legendre (1808, p. 394).) ►This result, first proved in Hadamard (1896) and de la Vallée Poussin (1896a, b), is known as the prime number theorem. … ►If , then the Euler–Fermat theorem states that …13: 20 Theta Functions
Chapter 20 Theta Functions
…14: Tom M. Apostol
…
►Apostol was born on August 20, 1923.
…
►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).
…
15: 1.12 Continued Fractions
16: 30.10 Series and Integrals
17: 10.44 Sums
…
►
§10.44(i) Multiplication Theorem
… ►§10.44(ii) Addition Theorems
►Neumann’s Addition Theorem
… ►Graf’s and Gegenbauer’s Addition Theorems
…18: 3.8 Nonlinear Equations
…
►Initial approximations to the zeros can often be found from asymptotic or other approximations to , or by application of the phase principle or Rouché’s theorem; see §1.10(iv).
…
…
►
3.8.15
…
►Consider and .
We have and .
…
19: Bibliography
…
►
Characterization theorems for orthogonal polynomials.
In Orthogonal Polynomials (Columbus, OH, 1989),
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. 294, pp. 1–24.
…
►
Monotonicity theorems and inequalities for the complete elliptic integrals.
J. Comput. Appl. Math. 172 (2), pp. 289–312.
…
►
Umbral calculus, Bailey chains, and pentagonal number theorems.
J. Combin. Theory Ser. A 91 (1-2), pp. 464–475.
…
►
Theorems on generalized Dedekind sums.
Pacific J. Math. 2 (1), pp. 1–9.
…
►
A Centennial History of the Prime Number Theorem.
In Number Theory,
Trends Math., pp. 1–14.
…
20: 19.35 Other Applications
…
►