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4 hours ago · In fact, the first measurement of parallax was possible only in 1839 by Friedrich Bessel. In the seventeenth century, Kepler suggested a clever way of testing the heliocentric theory. He argued that two stars which appear to be very close in the sky are, except in very rare cases, must be actually far away from each other.
4 days ago · Parallax is a fascinating phenomenon that occurs when objects appear to shift their position due to a change in perspective. These 13 astounding facts about parallax have shed light on this intriguing optical effect.
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5 days ago · Bessel generating functions. Peter Andreas Hansen (1795--1874), a German astronomer, was the first who discovered in 1843 the generating function for the Bessel functions of the first kind: ex(z−1/z)/2 = ∑n=−∞∞ znJn(x) e x ( z − 1 / z) / 2 = ∑ n = − ∞ ∞ z n J n ( x)
2 days ago · In this section, we show that Bessel's functions \[ \phi_n (x) = J_{ u} \left( \mu_n \frac{x}{\ell} \right) \qquad (n=1,2,3,\ldots ) \] are orthogonal when parameters μ n are positive roots of some transcendent equation involving Bessel functions of the first kind.
4 days ago · This secton is devoted to one of the most important differential equations---Bessel equation. Its solutions were named for Friedrich Wilhelm Bessel (1784--1846); however, Daniel Bernoulli is generally credited with being the first to introduce the concept of Bessels functions in 1732.
2 days ago · With equation (4), derived by Friedrich Bessel in 1826, the situation is improved. h 1 + h 2, being the distance between the knife edges, can be measured accurately. h 1 – h 2 is more difficult to measure accurately, because accurate location of the centre of mass G is difficult.
