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11: 19.36 Methods of Computation

… ►The step from

n

n+1

is an ascending Landen transformation if

\theta=1

(leading ultimately to a hyperbolic case of

R_{C}

) or a descending Gauss transformation if

\theta=-1

(leading to a circular case of

R_{C}

). … ►If

\alpha^{2}=k^{2}

, then the method fails, but the function can be expressed by (19.6.13) in terms of

E\left(\phi,k\right)

, 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

… ►

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MacDonald (1989) tabulates the first 30 zeros, in ascending order of absolute value in the fourth quadrant, of the function $J_{0}\left(z\right)-iJ_{1}\left(z\right)$ , 6D. (Other zeros of this function can be obtained by reflection in the imaginary axis).

…