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Vor 5 Tagen · In mathematics, a generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by n is a rational function of n. The series, if convergent, defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by analytic continuation.
Vor 5 Tagen · This section is about Bessel's equation and its solutions, known as Bessel functions or cylinder functions. The origin of the term cylinder is due to the fact that these functions are encountered in studying the boundary–value problems of potential theory for cylindrical coordi-nates.
Vor 3 Tagen · In this section, we show that Bessel's functions \[ \phi_n (x) = J_{\nu} \left( \mu_n \frac{x}{\ell} \right) \qquad (n=1,2,3,\ldots ) \] are orthogonal when parameters μ n are positive roots of some transcendent equation involving Bessel functions of the first kind.
Vor 4 Tagen · Orthogonality of Bessel's functions. Since expansions over Bessel functions depends on their orthogonality, we recall the basic formula that was derived in section of Part VII. Let α and β be arbitrary positive real numbers. Then for ν > −1, we have. (α2 − β2)∫ℓ0Jν(αx)Jν(βx)xdx = ℓ[αJ ′ ν(αℓ)Jν(βℓ) − βJ ′ ν(βℓ), Jν(αℓ)], ν > − 1.
Vor 5 Tagen · Als Bessel-Verfahren oder Bessel-Methode wird eine Messmethode zur Bestimmung der Brennweite $ f $ einer Sammellinse bezeichnet. Sie ist benannt nach Friedrich Wilhelm Bessel , der sie im Jahre 1840 publizierte.
Vor 2 Tagen · Genus Astrodiscus Schulze, 1875 accepted as Astrorhiza Sandahl, 1858 (Junior homonym of Astrodiscus Ludwig, 1866) Genus Astrorhizinella Saidova, 1970 accepted as Psammina Haeckel, 1889 (Subjective junior synonym Opinion of Tendal (1996), Kamenskaya and Saidova (1998)) Genus Globosiphon Avnimelech, 1952 accepted as Pelosina Brady, 1879.
Vor 5 Tagen · On completion, the combined business, known as Markerstudy, will provide multiple insurance products to millions of consumers, including home and motor insurance, and will employ around 7,000 people across the UK.
