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1: 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)). …
2: 30.10 Series and Integrals
For an addition theorem, see Meixner and Schäfke (1954, p. 300) and King and Van Buren (1973). …
3: 10.44 Sums
§10.44(ii) Addition Theorems
Neumann’s Addition Theorem
Graf’s and Gegenbauer’s Addition Theorems
4: 22.18 Mathematical Applications
§22.18(iv) Elliptic Curves and the Jacobi–Abel Addition Theorem
With the identification x = sn ( z , k ) , y = d ( sn ( z , k ) ) / d z , 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). …
5: 10.23 Sums
§10.23(ii) Addition Theorems
Neumann’s Addition Theorem
Graf’s and Gegenbauer’s Addition Theorems
See accompanying text
Figure 10.23.1: Graf’s and Gegenbauer’s addition theorems. Magnify
6: 14.28 Sums
§14.28(i) Addition Theorem
7: 13.13 Addition and Multiplication Theorems
§13.13 Addition and Multiplication Theorems
§13.13(i) Addition Theorems for M ( a , b , z )
§13.13(ii) Addition Theorems for U ( a , b , z )
13.13.12 e y ( x + y x ) 1 - b n = 0 ( - y ) n n ! x n U ( a - n , b - n , x ) , | y | < | x | .
8: 12.13 Sums
§12.13(i) Addition Theorems
9: 23.23 Tables
05, and in the case of ( z ) the user may deduce values for complex z by application of the addition theorem (23.10.1). …
10: 13.26 Addition and Multiplication Theorems
§13.26 Addition and Multiplication Theorems
§13.26(i) Addition Theorems for M κ , μ ( z )
§13.26(ii) Addition Theorems for W κ , μ ( z )