q-binomial%20series
(0.003 seconds)
11—20 of 336 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: 20 Theta Functions
Chapter 20 Theta Functions
…13: 7.24 Approximations
…
►
•
…
►
•
►
•
…
Cody (1969) provides minimax rational approximations for and . The maximum relative precision is about 20S.
Cody et al. (1970) gives minimax rational approximations to Dawson’s integral (maximum relative precision 20S–22S).
§7.24(ii) Expansions in Chebyshev Series
… ►Shepherd and Laframboise (1981) gives coefficients of Chebyshev series for on (22D).
14: 25.12 Polylogarithms
…
►The cosine series in (25.12.7) has the elementary sum
…
►For real or complex and the polylogarithm
is defined by
…
►For each fixed complex the series defines an analytic function of for .
The series also converges when , provided that .
…
►The notation was used for in Truesdell (1945) for a series treated in Jonquière (1889), hence the alternative name Jonquière’s function.
…
15: 6.16 Mathematical Applications
…
►Consider the Fourier series
…
►Compare Figure 6.16.1.
…
►It occurs with Fourier-series expansions of all piecewise continuous functions.
…
…
►
16: Tom M. Apostol
…
►Apostol was born on August 20, 1923.
…
►He was internationally known for his textbooks on calculus, analysis, and analytic number theory, which have been translated into five languages, and for creating Project
MATHEMATICS!, a series of video programs that bring mathematics to life with computer animation, live action, music, and special effects.
…
17: 17.16 Mathematical Applications
§17.16 Mathematical Applications
►Many special cases of -series arise in the theory of partitions, a topic treated in §§27.14(i) and 26.9. In Lie algebras Lepowsky and Milne (1978) and Lepowsky and Wilson (1982) laid foundations for extensive interaction with -series. …18: 23.9 Laurent and Other Power Series
19: 4.47 Approximations
…
►
§4.47(i) Chebyshev-Series Expansions
…20: Bibliography V
…
►
On the series expansion method for computing incomplete elliptic integrals of the first and second kinds.
Math. Comp. 23 (105), pp. 61–69.
…
►
An infinite series of Weber’s parabolic cylinder functions.
Proc. Benares Math. Soc. (N.S.) 3, pp. 37.
…
►
Some novel infinite series of spherical Bessel functions.
Quart. Appl. Math. 42 (3), pp. 321–324.
…
►
Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation.
Constr. Approx. 20 (1), pp. 39–54.
…
►
Fourier series representation of Ferrers function
.
…