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11: 19.36 Methods of Computation
The step from n to n + 1 is an ascending Landen transformation if θ = 1 (leading ultimately to a hyperbolic case of R C ) or a descending Gauss transformation if θ = - 1 (leading to a circular case of R C ). … If α 2 = k 2 , then the method fails, but the function can be expressed by (19.6.13) in terms of E ( ϕ , k ) , for which Neuman (1969b) uses ascending Landen transformations. …
12: 18.21 Hahn Class: Interrelations
See accompanying text
Figure 18.21.1: Askey scheme. …It increases by one for each row ascended in the scheme, culminating with four free real parameters for the Wilson and Racah polynomials. … Magnify
13: 10.75 Tables
  • MacDonald (1989) tabulates the first 30 zeros, in ascending order of absolute value in the fourth quadrant, of the function J 0 ( z ) - i J 1 ( z ) , 6D. (Other zeros of this function can be obtained by reflection in the imaginary axis).