1 ] {\displaystyle [0,1]} . The moment problem also extends to complex analysis as the trigonometric moment problem in which the Hankel matrices are...

In mathematics, the trigonometric moment problem is formulated as follows: given a sequence { c k } k ∈ N 0 {\displaystyle \{c_{k}\}_{k\in \mathbb {N}...

of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a...

variables Moment problem Hamburger moment problem Carleman's condition Hausdorff moment problem Trigonometric moment problem Stieltjes moment problem Prior...

_{k=1}^{\infty }k\left|{\widehat {c}}_{k}\right|^{2}\right).} Trigonometric moment problem Verblunsky's theorem Böttcher, Albrecht; Silbermann, Bernd (1990)...

are an example of orthogonal polynomials on the unit circle. Trigonometric moment problem Schur class Simon 2005a, p. 43. Simon 2010, p. 44. Simon 2010...

Standard deviation / (1:DCR) Standardized moment / (1:R) Stieltjes moment problem / anl (1:R) Trigonometric moment problem / anl (1:R) Uncorrelated / (2:R) Variance /...

}}(\xi )\,d\xi =\nu (\{0\}).} Lebesgue's decomposition theorem Trigonometric moment problem Furstenberg's Conjecture on 2-3-invariant continuous probability...

the problem can be solved analytically, i.e., in terms of well-studied functions such as trigonometric functions. The solution of this problem is important...

others. He developed trigonometry and constructed trigonometric tables, and he solved several problems of spherical trigonometry. With his solar and lunar...

(2)=\sum _{k=1}^{\infty }{\frac {1}{k^{2}}}={\frac {\pi ^{2}}{6}}} (the Basel problem) ζ ( 4 ) = ∑ k = 1 ∞ 1 k 4 = π 4 90 {\displaystyle \zeta (4)=\sum _{k=1}^{\infty...

methods of functional analysis. In the early 1920s, he worked on the moment problem, to which he introduced the operator-theoretic approach by proving the...

In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points....

{1}{d}}\log _{10}c}.} Trigonometric calculations were facilitated by tables that contained the common logarithms of trigonometric functions. Another critical...

polyhedra. Pacific J. Math. 132 (1988), no. 1, 35–62. K. Schmüdgen. "The K-moment problem for compact semi-algebraic sets". Math. Ann. 289 (1991), no. 2, 203–206...

example is truncated power series representations of sin(x) and related trigonometric functions. For instance, taking only data from near the x = 0, we may...

the forward and inverse Zernike transform use symmetry properties of trigonometric functions, separability of radial and azimuthal parts of Zernike polynomials...

reported the discovery of the Lamb shift, the measurement of the magnetic moment of the electron, and Robert Marshak's two-meson hypothesis. Bethe took the...

allows the exact calculation (hisab) of the qibla using a spherical trigonometric formula that takes the coordinates of a location and of the Kaaba as...

+r_{2}^{2}-2r_{1}r_{2}\cos \Delta \theta ,\end{aligned}}} using the trigonometric product-to-sum formulas. This formula is the law of cosines, sometimes...

n in the nth derived set Sn of a set S of zeros of a trigonometric series. Given a trigonometric series f(x) with S as its set of zeros, Cantor had discovered...

applied to the argument x. He also introduced the modern notation for the trigonometric functions, the letter e for the base of the natural logarithm (now also...

(5): 616–620, ISSN 0002-9920, MR 2509066 Zygmund, A. (2002) [1935], Trigonometric Series. Vol. I, II, Cambridge Mathematical Library (3rd ed.), Cambridge...

markets. For example, there are scientific calculators, which include trigonometric and statistical calculations. Some calculators even have the ability...

In astronomy, an epoch or reference epoch is a moment in time used as a reference point for some time-varying astronomical quantity. It is useful for the...

childless and unmarried. To avoid this fate, he ascertained an auspicious moment for his daughter's wedding. To alert his daughter at the correct time, he...

ISSN 0065-1036. Kolesnik, G. A. (1973). "On the estimation of some trigonometric sums". Acta Arithmetica (in Russian). 25 (1): 7–30. ISSN 0065-1036....

navigational computation that uses compass direction, distance and a simple trigonometric table known as the toleta de marteloio. The rule told mariners how to...

entire degree. The clearing correction for parallax and refraction is a trigonometric function of the observed lunar distance and the altitudes of the two...

non-rigorous method, resembling differentiation, applicable to some trigonometric functions. Madhava of Sangamagrama and the Kerala School of Astronomy...