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19 relations: Alternating permutation, Carl Johan Malmsten, Catalan's constant, Complex plane, Dirichlet character, Dirichlet L-function, Dirichlet series, Euler number, Euler product, Functional equation (L-function), Gamma function, Hurwitz zeta function, Lerch zeta function, Mathematics, On-Line Encyclopedia of Integer Sequences, Polygamma function, Prime number, Riemann zeta function, Special functions.
Alternating permutation
In combinatorial mathematics, an alternating permutation (or zigzag permutation) of the set is an arrangement of those numbers so that each entry is alternately greater or less than the preceding entry.
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Carl Johan Malmsten
Carl Johan Malmsten (April 9, 1814 in Uddetorp, Skara County, Sweden – February 11, 1886 in Uppsala, Sweden) was a Swedish mathematician and politician.
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Catalan's constant
In mathematics, Catalan's constant, which appears in combinatorics, is defined by where is the Dirichlet beta function.
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Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.
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Dirichlet character
In number theory, Dirichlet characters are certain arithmetic functions which arise from completely multiplicative characters on the units of \mathbb Z / k \mathbb Z. Dirichlet characters are used to define Dirichlet ''L''-functions, which are meromorphic functions with a variety of interesting analytic properties.
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Dirichlet L-function
In mathematics, a Dirichlet L-series is a function of the form Here χ is a Dirichlet character and s a complex variable with real part greater than 1.
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Dirichlet series
In mathematics, a Dirichlet series is any series of the form where s is complex, and a_n is a complex sequence.
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Euler number
In mathematics, the Euler numbers are a sequence En of integers defined by the Taylor series expansion where is the hyperbolic cosine.
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Euler product
In number theory, an Euler product is an expansion of a Dirichlet series into an infinite product indexed by prime numbers.
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Functional equation (L-function)
In mathematics, the L-functions of number theory are expected to have several characteristic properties, one of which is that they satisfy certain functional equations.
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Gamma function
In mathematics, the gamma function (represented by, the capital Greek alphabet letter gamma) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers.
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Hurwitz zeta function
In mathematics, the Hurwitz zeta function, named after Adolf Hurwitz, is one of the many zeta functions.
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Lerch zeta function
In mathematics, the Lerch zeta function, sometimes called the Hurwitz–Lerch zeta-function, is a special function that generalizes the Hurwitz zeta function and the polylogarithm.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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On-Line Encyclopedia of Integer Sequences
The On-Line Encyclopedia of Integer Sequences (OEIS), also cited simply as Sloane's, is an online database of integer sequences.
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Polygamma function
In mathematics, the polygamma function of order is a meromorphic function on '''ℂ''' and defined as the th derivative of the logarithm of the gamma function: Thus holds where is the digamma function and is the gamma function.
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Prime number
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
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Riemann zeta function
The Riemann zeta function or Euler–Riemann zeta function,, is a function of a complex variable s that analytically continues the sum of the Dirichlet series which converges when the real part of is greater than 1.
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Special functions
Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications.
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Catalan beta function, Dirichlet beta.
