Bickley–Naylor Functions
In physics, engineering, and applied mathematics, the Bickley–Naylor functions are a sequence of special functions arising in formulas for thermal radiation intensities in hot enclosures. The solutions are often quite complicated unless the problem is essentially one-dimensional (such as the radiation field in a thin layer of gas between two parallel rectangular plates). These functions have practical applications in several engineering problems related to transport of thermal or neutron, radiation in systems with special symmetries (e.g. spherical or axial symmetry). W. G. Bickley was a British mathematician born in 1893. Definition The ''n''th Bickley−Naylor function \operatorname_n(x) is defined by : \operatorname_n (x) = \int_0^ e^\cos^\theta \, d\theta. and it is classified as one of the generalized exponential integral functions. All of the functions \operatorname_n(x) for positive integer ''n'' are monotonously decreasing functions, because e^ is a decreasing func ...
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