representations by Euler?Maclaurin formula
(0.012 seconds)
1—10 of 345 matching pages
1: Wolter Groenevelt
…
►Groenevelt’s research interests is in special functions and orthogonal polynomials and their relations with representation theory and interacting particle systems.
►As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials.
…
2: 18.10 Integral Representations
3: 1.17 Integral and Series Representations of the Dirac Delta
§1.17 Integral and Series Representations of the Dirac Delta
… ►§1.17(ii) Integral Representations
… ►Then comparison of (1.17.2) and (1.17.9) yields the formal integral representation … ►Sine and Cosine Functions
… ►§1.17(iii) Series Representations
…4: 21.10 Methods of Computation
…
►
•
►
•
►
•
Tretkoff and Tretkoff (1984). Here a Hurwitz system is chosen to represent the Riemann surface.
Deconinck and van Hoeij (2001). Here a plane algebraic curve representation of the Riemann surface is used.
5: Bibliography V
…
►
Representation of Lie Groups and Special Functions. Volume 2: Class I Representations, Special Functions, and Integral Transforms.
Mathematics and its Applications (Soviet Series), Vol. 74, Kluwer Academic Publishers Group, Dordrecht.
►
Special Functions and the Theory of Group Representations.
American Mathematical Society, Providence, RI.
►
Representation of an odd number as a sum of three primes (Russian).
Dokl. Akad. Nauk SSSR 15, pp. 169–172 (Russian).
…
►
Integral representations for products of Lamé functions by use of fundamental solutions.
SIAM J. Math. Anal. 15 (3), pp. 559–569.
…
►
Fourier series representation of Ferrers function
.
…
6: 26.19 Mathematical Applications
§26.19 Mathematical Applications
… ►Partitions and plane partitions have applications to representation theory (Bressoud (1999), Macdonald (1995), and Sagan (2001)) and to special functions (Andrews et al. (1999) and Gasper and Rahman (2004)). …7: 35.9 Applications
…
►These references all use results related to the integral formulas (35.4.7) and (35.5.8).
►For applications of the integral representation (35.5.3) see McFarland and Richards (2001, 2002) (statistical estimation of misclassification probabilities for discriminating between multivariate normal populations).
…
8: 18.5 Explicit Representations
§18.5 Explicit Representations
… ►Chebyshev
… ►§18.5(ii) Rodrigues Formulas
… ►Related formula: … ►9: 27.13 Functions
…
►Each representation of as a sum of elements of is called a partition of , and the number of such partitions is often of great interest.
…
►A general formula states that
…
►
§27.13(iv) Representation by Squares
… ►In fact, there are four representations, given by , and four more with the order of summands reversed. … ►Also, Milne (1996, 2002) announce new infinite families of explicit formulas extending Jacobi’s identities. …10: 14.21 Definitions and Basic Properties
…
►When is complex , , and are defined by (14.3.6)–(14.3.10) with replaced by : the principal branches are obtained by taking the principal values of all the multivalued functions appearing in these representations when , and by continuity elsewhere in the -plane with a cut along the interval ; compare §4.2(i).
…
►