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  2. Dirichlet eta function - Wikipedia

    en.wikipedia.org/wiki/Dirichlet_eta_function

    Color representation of the Dirichlet eta function. It is generated as a Matplotlib plot using a version of the Domain coloring method. [1]In mathematics, in the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any complex number having real part > 0: = = = + +.

  3. Dedekind eta function - Wikipedia

    en.wikipedia.org/wiki/Dedekind_eta_function

    Dedekind η-function in the upper half-plane. In mathematics, the Dedekind eta function, named after Richard Dedekind, is a modular form of weight 1/2 and is a function defined on the upper half-plane of complex numbers, where the imaginary part is positive. It also occurs in bosonic string theory.

  4. Eta function - Wikipedia

    en.wikipedia.org/wiki/Eta_function

    In mathematics, eta function may refer to: The Dirichlet eta function η(s), a Dirichlet series; The Dedekind eta function η(τ), a modular form; The Weierstrass eta function η(w) of a lattice vector; The eta function η(s) used to define the eta invariant

  5. Greek letters used in mathematics, science, and engineering

    en.wikipedia.org/wiki/Greek_letters_used_in...

    the Eta function of Ludwig Boltzmann's H-theorem ("Eta" theorem), in statistical mechanics; Information theoretic (Shannon) entropy; represents: the intrinsic wave impedance of a medium (e.g. the impedance of free space)

  6. Eta - Wikipedia

    en.wikipedia.org/wiki/Eta

    Eta in the function of /h/ on an Attic red-figured calyx-krater, 515 BC. Amongst the depicted figures are Hermes and Hypnos. Inscriptions: ... Statistics, η 2 is the ...

  7. Beta distribution - Wikipedia

    en.wikipedia.org/wiki/Beta_distribution

    In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1) in terms of two positive parameters, denoted by alpha (α) and beta (β), that appear as exponents of the variable and its complement to 1, respectively, and control the shape of the distribution.

  8. Kronecker limit formula - Wikipedia

    en.wikipedia.org/wiki/Kronecker_limit_formula

    In mathematics, the classical Kronecker limit formula describes the constant term at s = 1 of a real analytic Eisenstein series (or Epstein zeta function) in terms of the Dedekind eta function. There are many generalizations of it to more complicated Eisenstein series. It is named for Leopold Kronecker.

  9. Chowla–Selberg formula - Wikipedia

    en.wikipedia.org/wiki/Chowla–Selberg_formula

    This has led to much research and generalization. In particular there is an analog of the Chowla–Selberg formula for p-adic numbers, involving a p-adic gamma function, called the Gross–Koblitz formula. The Chowla–Selberg formula gives a formula for a finite product of values of the eta functions.