elliptic integrals
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31—40 of 132 matching pages
31: 19.11 Addition Theorems
32: 22.16 Related Functions
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►In Equations (22.16.21)–(22.16.23),
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►In Equations (22.16.24)–(22.16.26), .
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►For see §19.2(ii).
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►For see §19.2(ii).
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Relation to the Elliptic Integral
…33: 19.8 Quadratic Transformations
34: 29.2 Differential Equations
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►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).
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29.2.8
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35: 29.18 Mathematical Applications
36: 22.14 Integrals
37: 29.12 Definitions
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►The superscript on the left-hand sides of (29.12.1)–(29.12.8) agrees with the number of -zeros of each Lamé polynomial in the interval , while is the number of -zeros in the open line segment from to .
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38: 29.8 Integral Equations
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►Let be any solution of (29.2.1) of period , be a linearly independent solution, and denote their Wronskian.
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29.8.2
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29.8.7
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39: 36.1 Special Notation
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►The main functions covered in this chapter are cuspoid catastrophes ; umbilic catastrophes with codimension three , ; canonical integrals
, , ; diffraction catastrophes , , generated by the catastrophes.
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