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List of mathematical series. This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. is a Bernoulli polynomial. is an Euler number. is the Riemann zeta function. is the gamma function. is a polygamma function. is a polylogarithm.
Connective constant for the hexagonal lattice [15][16] μ {\displaystyle \mu } 1.84775 90650 22573 51225 [Mw 7][OEIS 12] 2 + 2 {\displaystyle {\sqrt {2+ {\sqrt {2}}}}} , as a root of the polynomial. x 4 − 4 x 2 + 2 = 0 {\displaystyle x^ {4}-4x^ {2}+2=0} 1593 [OEIS 12] .
The gamma function is the unique function that simultaneously satisfies. , for all complex numbers except the non-positive integers, and, for integer n, for all complex numbers . [1] In a certain sense, the log-gamma function is the more natural form; it makes some intrinsic attributes of the function clearer.
Aspect ratio (image) The aspect ratio of an image is the ratio of its width to its height. It is expressed as two numbers separated by a colon, width:height. Common aspect ratios are 1.85:1 and 2.40:1 in cinematography, 4:3 and 16:9 in television, and 3:2 in still photography.
Calculus. In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions: The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it ...
It is unknown whether these constants are transcendental in general, but Γ( 1 / 3 ) and Γ( 1 / 4 ) were shown to be transcendental by G. V. Chudnovsky. Γ( 1 / 4 ) / 4 √ π has also long been known to be transcendental, and Yuri Nesterenko proved in 1996 that Γ( 1 / 4 ), π, and e π are algebraically independent.
The alternative Super series, denoted SnR, nR Plus or nR+, has an aspect ratio of 3∶2 (or as close as possible) and thus provides a better fit for standard 135 film (35 mm) at sizes of 8 inches or above. 5R is twice the size of a 2R print, 6R twice the size of a 4R print and S8R twice the size of 6R. 4D/6D is a newer size for most consumer ...
1/2 + 1/4 + 1/8 + 1/16 + ⋯. First six summands drawn as portions of a square. The geometric series on the real line. In mathematics, the infinite series 1 2 + 1 4 + 1 8 + 1 16 + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1. In summation notation ...