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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 is a ...
The Planck relation [1] [2] [3] (referred to as Planck's energy–frequency relation, [4] the Planck–Einstein relation, [5] Planck equation, [6] and Planck formula, [7] though the latter might also refer to Planck's law [8] [9]) is a fundamental equation in quantum mechanics which states that the energy E of a photon, known as photon energy, is proportional to its frequency ν: =.
The Hughes H-1 Racer is a racing aircraft built by Hughes Aircraft in 1935. Utilizing different wings, it set both a world airspeed record and a transcontinental speed record across the United States. The H-1 Racer was the last aircraft built by a private individual to set the world speed record; most aircraft to hold the record since have been ...
Euler's constant (sometimes called the Euler–Mascheroni constant) is a mathematical constant, usually denoted by the lowercase Greek letter gamma ( γ ), defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by log : Here, ⌊·⌋ represents the floor function .
By this construction, the function that defines the harmonic number for complex values is the unique function that simultaneously satisfies (1) H 0 = 0, (2) H x = H x−1 + 1/x for all complex numbers x except the non-positive integers, and (3) lim m→+∞ (H m+x − H m) = 0 for all complex values x.
Born in Neath, Glamorganshire, Wales, Price was educated at Winchester College and New College, Oxford. He obtained first-class honours in Literae Humaniores in 1921. He was a Fellow of Magdalen College, Oxford, 1922–4, Assistant Lecturer in philosophy at the university of Liverpool (1922–23), Fellow and Tutor of Trinity College, Oxford ...
e. The number e is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways. It is the base of the natural logarithm function. It is the limit of as n tends to infinity, an expression that arises in the computation of compound interest.
Ali Hasan Nayfeh ( Arabic: علي نايفة) (21 December 1933 – 27 March 2017) [ 1] was a Palestinian - Jordanian mathematician, mechanical engineer and physicist. [ 2] He is regarded as the most influential scholar and scientist in the area of applied nonlinear dynamics in mechanics and engineering. [ 3] He was the inaugural winner of the ...