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Function Gegenbauer

Their solution, involving Gegenbauer functions, resulted in a wall correction factor for rigid spheres which is the same as the full expression corresponding to Eq. (32). [Pg.66]

These polynomial functions are closely related to the so-called Gegenbauer polynomials16 and satisfy the orthogonality condition... [Pg.461]

Because the general solution (7 131) is expressed in terms of the modified Gegenbauer polynomials Q (r]), it is convenient to also express (7 146) in terms of these functions. Referring to definitions (7 132), we see that (7 146) can also be expressed in the form... [Pg.465]

The Gegenbauer functions of the first kind are polynomials and can be represented in the form... [Pg.57]

The Gegenbauer functions of the second kind are given by the formulas... [Pg.57]

For n > 2, the Gegenbauer functions of the second kind are infinite at the points = 1, which correspond to 6 = 0 and 9 = it. Therefore, if there are no singularities in the physical statement of the problem, then all the constants with tildes in (2.1.5) must be zero. Moreover, for n = 0 and n = 1, the remaining constants, if nonzero, result in infinite values of the tangential velocity Vg on... [Pg.57]

Like the Legendre polynomials, the Gegenbauer polynomials are found by expanding the generating function in a Taylor series, and collecting... [Pg.149]

The resonance energy calculated up to Mth-order as a function of M is shown below. Note the oscillatory convergence towards the exact value of 2. The method used above to obtain 5," for n = 2,3,4 becomes extremely laborious for larger n. The results below were calculated by first showing that = 4PC where Q Gegenbauer polynomial of degree... [Pg.347]


See other pages where Function Gegenbauer is mentioned: [Pg.239]    [Pg.239]    [Pg.55]    [Pg.57]    [Pg.57]    [Pg.148]    [Pg.140]    [Pg.149]   
See also in sourсe #XX -- [ Pg.57 ]




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