Harold Exton

	Harold Exton Harold Exton is a mathematician at University of Central Lancashire (called Preston Polytechnic while he was there) working on hypergeometric functions, who introduced the Hahn–Exton q-Bessel function In mathematics, the Hahn–Exton ''q''-Bessel function or the third Jackson q-Bessel function, Jackson ''q''-Bessel function is a q-analog, ''q''-analog of the Bessel function, and satisfies the Hahn-Exton ''q''-difference equation (). This functio .... References * * * English mathematicians Living people Year of birth missing (living people) {{UK-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	University Of Central Lancashire , mottoeng = "From the Earth to the Sun" , established = as Institution for the Diffusion of Useful Knowledgere-established 1992 (University status granted) , type = Public , chancellor = Ranvir Singh , vice_chancellor = Graham Baldwin , students = () , undergrad = () , postgrad = () , city = Preston (Main)BurnleyCyprusWestlakes, Cumbria , campus = Urban , former_names = Harris Art College, Preston Polytechnic, Lancashire Polytechnic , colours = , website = , logo = , logo_caption = , logo_size = , footnotes = , affiliations = University AllianceUniversities UK , coor = , pushpin_map = United Kingdom Preston central The University of Central Lancashire (abbrevi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Hahn–Exton Q-Bessel Function In mathematics, the Hahn–Exton ''q''-Bessel function or the third Jackson q-Bessel function, Jackson ''q''-Bessel function is a q-analog, ''q''-analog of the Bessel function, and satisfies the Hahn-Exton ''q''-difference equation (). This function was introduced by in a special case and by in general. The Hahn–Exton ''q''-Bessel function is given by : J_\nu^(x;q) = \frac \sum_\frac= \frac x^\nu _1\phi_1(0;q^;q,qx^2). \phi is the basic hypergeometric function. Properties Zeros Koelink and Swarttouw proved that J_\nu^(x;q) has infinite number of real zeros. They also proved that for \nu>-1 all non-zero roots of J_\nu^(x;q) are real (). For more details, see and . Zeros of the Hahn-Exton ''q''-Bessel function appear in a discrete analog of Daniel Bernoulli's problem about free vibrations of a lump loaded chain (, ) Derivatives For the (usual) derivative and ''q''-derivative of J_\nu^(x;q), see . The symmetric ''q''-derivative of J_\nu^(x;q) is described on . Recurrence R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
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