general elliptic integrals
(0.008 seconds)
21—30 of 70 matching pages
21: 23.7 Quarter Periods
22: 19.26 Addition Theorems
§19.26 Addition Theorems
►§19.26(i) General Formulas
… ►An equivalent version for is … ►§19.26(iii) Duplication Formulas
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19.26.21
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23: 19.17 Graphics
§19.17 Graphics
►See Figures 19.17.1–19.17.8 for symmetric elliptic integrals with real arguments. ►Because the -function is homogeneous, there is no loss of generality in giving one variable the value or (as in Figure 19.3.2). …The cases or correspond to the complete integrals. … ►To view and for complex , put , use (19.25.1), and see Figures 19.3.7–19.3.12. …24: 29.2 Differential Equations
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►For see §22.2.
This equation has regular singularities at the points , where , and , are the complete elliptic integrals of the first kind with moduli , , respectively; see §19.2(ii).
In general, at each singularity each solution of (29.2.1) has a branch point (§2.7(i)).
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§29.2(ii) Other Forms
… ►we have …25: 19.16 Definitions
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§19.16(i) Symmetric Integrals
… ►The -function is often used to make a unified statement of a property of several elliptic integrals. … … ►§19.16(iii) Various Cases of
… ►All other elliptic cases are integrals of the second kind. …26: 23.4 Graphics
27: Bibliography F
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Calculation of elliptic integrals of the third kind by means of Gauss’ transformation.
Math. Comp. 19 (89), pp. 97–104.
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On the reciprocal modulus relation for elliptic integrals.
SIAM J. Math. Anal. 1 (4), pp. 524–526.
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Numerical evaluation of the elliptic integral of the third kind.
Math. Comp. 19 (91), pp. 494–496.
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Series expansions of symmetric elliptic integrals.
Math. Comp. 81 (278), pp. 957–990.
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Generalized Fermi-Dirac integrals—FD, FDG, FDH.
Comput. Phys. Comm. 39 (2), pp. 181–185.
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28: 15.17 Mathematical Applications
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