Hermann Hankel

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The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Hankel, Hermann


Born Feb. 14, 1839, in Halle; died Aug. 29, 1873, in Schramberg. German mathematician.

Working in Erlangen and Tübingen, he derived a series of formulas on the theory of cylindrical functions; his researches on the foundations of arithmetic promoted the development of the theory of quaternions and general hyper-complex number systems. Hankel also wrote works on the history of mathematics in the classical and medieval periods.


Theorie der complexen Zahlensysteme. Leipzig, 1867. (Vorlesungen über die complexen Zahlen und ihre Funktionen, part 1.)
Zur Geschichte der Mathematick in Altertum und Mittelalter. Leipzig, 1874.
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
So we can attain rank([X.sub.e]) = [L.sub.p] [greater than or equal to] rank(X), [X.sub.e] is a K x (M - K +1) Hankel block matrix, and [X.sub.m] is a Px(N -P + 1) Hankel matrix, K and P are the two window parameters, which can be adjusted to increase the estimation accuracy.
Now, we introduce the Hankel determinant for the [k.sup.th] root transform for the function f given in (1.1) for the values q, n, k [member of] N = {1, 2, 3,...} defined as
Anyone who wants you to live in misery for their happiness should not be in your life to begin with,' said the quote attributed to author Isaiah Hankel.
Hankel matrices have been used in the related contexts for more than a century by many authors; see, e.g., the seminal paper by Stieltjes [53, Sections 8-11, p.
Zheng, "The distribution function inequality and products of Toeplitz operators and Hankel operators," Journal of Functional Analysis, vol.
In order to simplify the calculation and improve the calculation accuracy, we design the input deletion strategy based on the zero space projection on the basis of block Hankel matrix and related data estimation separately [20].
There are several choices for the two independent functions: Bessel [J.sub.m]([k.sub.i]) and Neumann [N.sub.m] functions or Hankel functions of the first [H.sup.(1).sub.m] and the second kind [H.sup.(2).sub.m].
The boundary value problems of a layered elastic half space under axisymmetric surface loading involving nonclassical boundary conditions due to surface stress influence are formulated by employing Love's strain potential and the Hankel integral transform.
It is noted that [v.sub.n](t) is zero-order finite Hankel transform of function v(r, t) and [u.sub.n](t) is the finite Hankel transform of the first order of function u(r, t), respectively.