(0.003 seconds)

## 1—10 of 168 matching pages

##### 1: 10.44 Sums
###### §10.44(i) Multiplication Theorem
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)). …
##### 4: 30.10 Series and Integrals
For an addition theorem, see Meixner and Schäfke (1954, p. 300) and King and Van Buren (1973). …
##### 5: 22.18 Mathematical Applications
###### §22.18(iv) Elliptic Curves and the Jacobi–Abel AdditionTheorem
For any two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ on this curve, their sum $(x_{3},y_{3})$, always a third point on the curve, is defined by the Jacobi–Abel addition law …With the identification $x=\operatorname{sn}\left(z,k\right)$, $y=\ifrac{\mathrm{d}(\operatorname{sn}\left(z,k\right))}{\mathrm{d}z}$, 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). …
##### 6: 13.13 Addition and Multiplication Theorems
###### §13.13(ii) AdditionTheorems for $U\left(a,b,z\right)$
13.13.12 $e^{y}\left(\frac{x+y}{x}\right)^{1-b}\sum_{n=0}^{\infty}\frac{(-y)^{n}}{n!x^{n% }}U\left(a-n,b-n,x\right),$ $|y|<|x|$.
##### 7: 14.28 Sums
###### §13.26(iii) Multiplication Theorems for $M_{\kappa,\mu}\left(z\right)$ and $W_{\kappa,\mu}\left(z\right)$
05, and in the case of $\wp\left(z\right)$ the user may deduce values for complex $z$ by application of the addition theorem (23.10.1). …