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Higher Transcendental Functions

01 Jan 1953-pp 59
About: The article was published on 1953-01-01 and is currently open access. It has received 3566 citations till now. The article focuses on the topics: Transcendental function.
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TL;DR: In this paper, the authors present an investigation of the massless, two-dimentional, interacting field theories and their invariance under an infinite-dimensional group of conformal transformations.

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TL;DR: In this paper, it was proved that the counterterm for an arbitrary 4-loop Feynman diagram in an arbitrary model is calculable within the minimal subtraction scheme in terms of rational numbers and the Riemann ζ-function in a finite number of steps via a systematic "algebraic" procedure involving neither integration of elementary, special, or any other functions, nor expansions in and summation of infinite series of any kind.

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TL;DR: In this paper, the prepotentials and geometry of the moduli spaces for a Calabi-Yau manifold and its mirror were derived and all the sigma model corrections to the Yukawa couplings and moduli space metric were obtained.

1,679 citations

Book
19 Mar 2001
TL;DR: In this article, the authors considered the properties of orthogonal polynomials on the unit sphere, root systems and Coxeter groups, and the Summability of Orthogonal expansions.
Abstract: Preface to the second edition Preface to the first edition 1. Background 2. Orthogonal polynomials in two variables 3. General properties of orthogonal polynomials in several variables 4. Orthogonal polynomials on the unit sphere 5. Examples of orthogonal polynomials in several variables 6. Root systems and Coxeter groups 7. Spherical harmonics associated with reflection groups 8. Generalized classical orthogonal polynomials 9. Summability of orthogonal expansions 10. Orthogonal polynomials associated with symmetric groups 11. Orthogonal polynomials associated with octahedral groups and applications References Author index Symbol index Subject index.

1,026 citations