Wynn cross rule

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41: 8.25 Methods of Computation

… ►See Allasia and Besenghi (1987b) for the numerical computation of

\Gamma\left(a,z\right)

from (8.6.4) by means of the trapezoidal rule. … ►A numerical inversion procedure is also given for calculating the value of

x

(with 10S accuracy), when

a

and

P\left(a,x\right)

are specified, based on Newton’s rule (§3.8(ii)). …

42: 9.17 Methods of Computation

… ►The trapezoidal rule (§3.5(i)) is then applied. … ►Zeros of the Airy functions, and their derivatives, can be computed to high precision via Newton’s rule (§3.8(ii)) or Halley’s rule (§3.8(v)), using values supplied by the asymptotic expansions of §9.9(iv) as initial approximations. …