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The Möbius function () is a multiplicative function in number theory introduced by the German mathematician August Ferdinand Möbius (also transliterated Moebius) in 1832. [i] [ii] [2] It is ubiquitous in elementary and analytic number theory and most often appears as part of its namesake the Möbius inversion formula.
For example, if one starts with Euler's totient function φ, and repeatedly applies the transformation process, one obtains: φ the totient function; φ ∗ 1 = I, where I(n) = n is the identity function; I ∗ 1 = σ 1 = σ, the divisor function; If the starting function is the Möbius function itself, the list of functions is: μ, the Möbius ...
Möbius syndrome or Moebius syndrome is a rare congenital neurological disorder which is characterized by facial paralysis and the inability to move the eyes from side to side. Most people with Möbius syndrome are born with complete facial paralysis and cannot close their eyes or form facial expressions.
The central idea of the method is expressed by the following identity, sometimes called the Legendre identity: (,) =; = | |,where A is a set of integers, P is a product of distinct primes, is the Möbius function, and is the set of integers in A divisible by d, and S(A, P) is defined to be:
The Möbius strip is one of the most famous objects in mathematics. Discovered in 1858 by two German mathematicians—August Ferdinand Möbius and Johann Benedict Listing—the Möbius strip is a ...
The following is a table of the Bell series of well-known arithmetic functions. The Möbius function has () =.; The Mobius function squared has () = +.; Euler's totient has () =.; The multiplicative identity of the Dirichlet convolution has () =
An oral glucose tolerance test checks how your body responds to glucose. Your blood glucose levels are measured before you consume 75 grams of glucose solution. Two hours later, your blood glucose ...
Riemann zeta function. Basel problem on ζ(2) Hurwitz zeta function; Bernoulli number. Agoh–Giuga conjecture; Von Staudt–Clausen theorem; Dirichlet series; Euler product; Prime number theorem. Prime-counting function. Meissel–Lehmer algorithm; Offset logarithmic integral; Legendre's constant; Skewes' number; Bertrand's postulate. Proof of ...