Neumann addition theorem
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1: 10.44 Sums
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§10.44(i) Multiplication Theorem
… ►§10.44(ii) Addition Theorems
►Neumann’s Addition Theorem
… ►Graf’s and Gegenbauer’s Addition Theorems
… ►§10.44(iii) Neumann-Type Expansions
…2: 28.27 Addition Theorems
§28.27 Addition Theorems
►Addition theorems provide important connections between Mathieu functions with different parameters and in different coordinate systems. They are analogous to the addition theorems for Bessel functions (§10.23(ii)) and modified Bessel functions (§10.44(ii)). …3: 10.23 Sums
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§10.23(ii) Addition Theorems
►Neumann’s Addition Theorem
… ►Graf’s and Gegenbauer’s Addition Theorems
… ► … ►Neumann’s Expansion
…4: 30.10 Series and Integrals
5: 22.18 Mathematical Applications
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§22.18(iv) Elliptic Curves and the Jacobi–Abel Addition Theorem
… ►For any two points and on this curve, their sum , always a third point on the curve, is defined by the Jacobi–Abel addition law …With the identification , , the addition law (22.18.8) is transformed into the addition theorem (22.8.1); see Akhiezer (1990, pp. 42, 45, 73–74) and McKean and Moll (1999, §§2.14, 2.16). …6: 13.13 Addition and Multiplication Theorems
§13.13 Addition and Multiplication Theorems
►§13.13(i) Addition Theorems for
… ►§13.13(ii) Addition Theorems for
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13.13.12
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§13.13(iii) Multiplication Theorems for and
…7: 14.28 Sums
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§14.28(i) Addition Theorem
… ►For generalizations in terms of Gegenbauer and Jacobi polynomials, see Theorem 2. 1 in Cohl (2013b) and Theorem 1 in Cohl (2013a) respectively. …8: 13.26 Addition and Multiplication Theorems
§13.26 Addition and Multiplication Theorems
►§13.26(i) Addition Theorems for
… ►§13.26(ii) Addition Theorems for
… ►§13.26(iii) Multiplication Theorems for and
…9: 12.13 Sums
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