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Elliptic integrals second kind

K and E are the full elliptic integrals, respectively, of the first and second kind with the modulus 1 /s/2 K was defined above, 2E K = 0.847. [Pg.312]

K, E and II being complete elliptic integrals of the first, second and third kind, respectively. According to Section 117.03 on Page 14 in Byrd and Friedman (1971) we have the formula... [Pg.70]

E and fl are complete elliptic integrals of the second and third kind in the standard notation of Byrd and Friedman [101]. This completes the explicit form of the Gross-Kohn approximation (191). [Pg.118]

In this case, the elliptic integral of the second kind is converted to a complete integral ... [Pg.364]

The total surface area related to the semimajor axis is a function of the two aspect ratios (3 and y. The special functions F(ty, k) and E(ty, k) are incomplete elliptical integrals of the first and second kind, respectively. They depend on the amplitude angle <[> and the modulus k. These special functions can be computed quickly and accurately by means of computer algebra systems such as Mathematica [153]. Their properties are given in Abramowitz and Stegun [1], The relationship between the square root of the total surface area and the semimajor axis is [150] ... [Pg.143]

Ei and Ea are the complete elliptical integrals of the second kind. These are evaluated using the arguments 1 - b2yia2 and 1 - b2la2, respectively. In addition, 6,/a, is related to to and m by means of the following ... [Pg.419]

E(m) complete elliptic integral of the second kind with argument m, which is... [Pg.422]

Appendix A. The elliptic integral of second kind Appendix B. The roots of equation (25)... [Pg.347]

See other pages where Elliptic integrals second kind is mentioned: [Pg.509]    [Pg.96]    [Pg.7]    [Pg.530]    [Pg.45]    [Pg.335]    [Pg.37]    [Pg.94]    [Pg.70]    [Pg.509]    [Pg.4]    [Pg.5]    [Pg.5]    [Pg.7]    [Pg.9]    [Pg.14]    [Pg.100]    [Pg.222]    [Pg.259]    [Pg.411]    [Pg.557]    [Pg.136]    [Pg.177]    [Pg.198]    [Pg.31]    [Pg.146]    [Pg.147]    [Pg.184]    [Pg.364]    [Pg.347]    [Pg.423]    [Pg.469]    [Pg.267]    [Pg.166]    [Pg.190]    [Pg.190]    [Pg.193]    [Pg.383]    [Pg.76]    [Pg.210]    [Pg.569]   
See also in sourсe #XX -- [ Pg.154 ]



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Elliptic integrals

Ellipticity

Second kind

The elliptic integral of second kind

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