# spheroidal wave functions

(0.006 seconds)

## 11—20 of 37 matching pages

##### 13: 30.16 Methods of Computation
###### §30.16(ii) SpheroidalWaveFunctions of the First Kind
30.16.9 $\mathsf{Ps}^{m}_{n}\left(x,\gamma^{2}\right)=\lim_{d\to\infty}\sum_{j=1}^{d}(-% 1)^{j-p}e_{j,d}\mathsf{P}^{m}_{n+2(j-p)}\left(x\right).$
##### 14: 31.12 Confluent Forms of Heun’s Equation
This has regular singularities at $z=0$ and $1$, and an irregular singularity of rank 1 at $z=\infty$. Mathieu functions (Chapter 28), spheroidal wave functions (Chapter 30), and Coulomb spheroidal functions30.12) are special cases of solutions of the confluent Heun equation. …
##### 15: 30.7 Graphics
###### §30.7(ii) Functions of the First Kind Figure 30.7.21: | Qs 0 0 ⁡ ( x + i ⁢ y , - 4 ) | , - 1.8 ≤ x ≤ 1.8 , - 2 ≤ y ≤ 2 . Magnify 3D Help
##### 16: 31.18 Methods of Computation
The computation of the accessory parameter for the Heun functions is carried out via the continued-fraction equations (31.4.2) and (31.11.13) in the same way as for the Mathieu, Lamé, and spheroidal wave functions in Chapters 2830.
##### 17: 30.8 Expansions in Series of Ferrers Functions
###### §30.8 Expansions in Series of Ferrers Functions
30.8.1 $\mathsf{Ps}^{m}_{n}\left(x,\gamma^{2}\right)=\sum_{k=-R}^{\infty}(-1)^{k}a^{m}% _{n,k}(\gamma^{2})\mathsf{P}^{m}_{n+2k}\left(x\right),$
##### 19: 30.14 Wave Equation in Oblate Spheroidal Coordinates
30.14.8 $w_{1}(\xi)=a_{1}S^{m(1)}_{n}\left(i\xi,\gamma\right)+b_{1}S^{m(2)}_{n}\left(i% \xi,\gamma\right).$
###### §30.14(v) The Interior Dirichlet Problem for Oblate Ellipsoids
30.14.9 $S^{m(1)}_{n}\left(\mathrm{i}\xi_{0},\gamma\right)=0.$