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  2. List of mathematical constants - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_constants

    The following list includes the continued fractions of some constants and is sorted by their representations. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one.

  3. Highly composite number - Wikipedia

    en.wikipedia.org/wiki/Highly_composite_number

    Order HCN n prime factorization prime exponents number of prime factors d(n) primorial factorization 1 1: 0 1 2 2* : 1 1 2 3 4: 2 2 3 4 6* : 1,1 2 4 5 12* : 2,1 3 6 6 24

  4. Minimum mean square error - Wikipedia

    en.wikipedia.org/wiki/Minimum_mean_square_error

    Standard method like Gauss elimination can be used to solve the matrix equation for .A more numerically stable method is provided by QR decomposition method. Since the matrix is a symmetric positive definite matrix, can be solved twice as fast with the Cholesky decomposition, while for large sparse systems conjugate gradient method is more effective.

  5. Simple continued fraction - Wikipedia

    en.wikipedia.org/wiki/Simple_continued_fraction

    The first term, as we see, is the first fraction; the first and second together give the second fraction, ⁠ 22 / 7 ⁠; the first, the second and the third give the third fraction ⁠ 333 / 106 ⁠, and so on with the rest; the result being that the series entire is equivalent to the original value.

  6. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    The roots of the quadratic function y = ⁠ 1 / 2 ⁠ x 2 − 3x + ⁠ 5 / 2 ⁠ are the places where the graph intersects the x-axis, the values x = 1 and x = 5.They can be found via the quadratic formula.

  7. Pi - Wikipedia

    en.wikipedia.org/wiki/Pi

    The number π (/ p aɪ / ⓘ; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter.It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.

  8. Factorial - Wikipedia

    en.wikipedia.org/wiki/Factorial

    Here () denotes the sum of the base-digits of , and the exponent given by this formula can also be interpreted in advanced mathematics as the p-adic valuation of the factorial. [54] Applying Legendre's formula to the product formula for binomial coefficients produces Kummer's theorem , a similar result on the exponent of each prime in the ...

  9. Prime number theorem - Wikipedia

    en.wikipedia.org/wiki/Prime_number_theorem

    In the first half of the twentieth century, some mathematicians (notably G. H. Hardy) believed that there exists a hierarchy of proof methods in mathematics depending on what sorts of numbers (integers, reals, complex) a proof requires, and that the prime number theorem (PNT) is a "deep" theorem by virtue of requiring complex analysis. [9]