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  2. Macdonald polynomials - Wikipedia

    en.wikipedia.org/wiki/Macdonald_polynomials

    If t=1 the Macdonald polynomials become the sums over W orbits, which are the monomial symmetric functions when the root system has type A. If we put t = q α and let q tend to 1 the Macdonald polynomials become Jack polynomials when the root system is of type A , and Heckman–Opdam polynomials for more general root systems.

  3. Ring of symmetric functions - Wikipedia

    en.wikipedia.org/wiki/Ring_of_symmetric_functions

    A ring of symmetric functions can be defined over any commutative ring R, and will be denoted Λ R; the basic case is for R = Z. The ring Λ R is in fact a graded R-algebra. There are two main constructions for it; the first one given below can be found in (Stanley, 1999), and the second is essentially the one given in (Macdonald, 1979).

  4. Macdonald identities - Wikipedia

    en.wikipedia.org/wiki/Macdonald_identities

    In mathematics, the Macdonald identities are some infinite product identities associated to affine root systems, introduced by Ian Macdonald . They include as special cases the Jacobi triple product identity , Watson's quintuple product identity , several identities found by Dyson (1972) , and a 10-fold product identity found by Winquist (1969) .

  5. Kontorovich–Lebedev transform - Wikipedia

    en.wikipedia.org/wiki/Kontorovich–Lebedev...

    In mathematics, the Kontorovich–Lebedev transform is an integral transform which uses a Macdonald function (modified Bessel function of the second kind) with imaginary index as its kernel. Unlike other Bessel function transforms, such as the Hankel transform, this transform involves integrating over the index of the function rather than its ...

  6. Ian G. Macdonald - Wikipedia

    en.wikipedia.org/wiki/Ian_G._Macdonald

    Ian Grant Macdonald FRS (11 October 1928 – 8 August 2023) was a British mathematician known for his contributions to symmetric functions, special functions, Lie algebra theory and other aspects of algebra, algebraic combinatorics, and combinatorics.

  7. Symbolab - Wikipedia

    en.wikipedia.org/wiki/Symbolab

    Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011.

  8. Macdonald conjecture - Wikipedia

    en.wikipedia.org/wiki/Macdonald_conjecture

    Macdonald conjecture may refer to one of several conjectures: Macdonald's conjectures about Macdonald polynomials Macdonald's generalization of the Dyson conjecture

  9. TI-BASIC 83 - Wikipedia

    en.wikipedia.org/wiki/TI-BASIC_83

    TI-BASIC 83,TI-BASIC Z80 or simply TI-BASIC, is the built-in programming language for the Texas Instruments programmable calculators in the TI-83 series. [1] Calculators that implement TI-BASIC have a built in editor for writing programs.