# joining factors

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## 5 matching pages

##### 1: 28.22 Connection Formulas
The joining factors in the above formulas are given by
28.22.5 $g_{\mathit{e},2m}(h)=(-1)^{m}\sqrt{\dfrac{2}{\pi}}\dfrac{\operatorname{ce}_{2m% }\left(\frac{1}{2}\pi,h^{2}\right)}{A_{0}^{2m}(h^{2})},$
28.22.9 $f_{\mathit{e},m}(h)=-\sqrt{\ifrac{\pi}{2}}g_{\mathit{e},m}(h){\operatorname{Mc% }^{(2)}_{m}}\left(0,h\right),$
28.22.10 $f_{\mathit{o},m}(h)=-\sqrt{\ifrac{\pi}{2}}g_{\mathit{o},m}(h){\operatorname{Ms% }^{(2)}_{m}}'\left(0,h\right),$
$\operatorname{ge}_{m}\left(0,h^{2}\right)=\tfrac{1}{2}\pi S_{m}(h^{2})\left(g_% {\mathit{o},m}(h)\right)^{2}\operatorname{se}_{m}'\left(0,h^{2}\right).$
##### 2: 28.1 Special Notation
The notation for the joining factors is …
$f_{\mathit{o},n}(h).$
##### 3: 28.35 Tables
• National Bureau of Standards (1967) includes the eigenvalues $a_{n}\left(q\right)$, $b_{n}\left(q\right)$ for $n=0(1)3$ with $q=0(.2)20(.5)37(1)100$, and $n=4(1)15$ with $q=0(2)100$; Fourier coefficients for $\operatorname{ce}_{n}\left(x,q\right)$ and $\operatorname{se}_{n}\left(x,q\right)$ for $n=0(1)15$, $n=1(1)15$, respectively, and various values of $q$ in the interval $[0,100]$; joining factors $g_{\mathit{e},n}(\sqrt{q})$, $f_{\mathit{e},n}(\sqrt{q})$ for $n=0(1)15$ with $q=0(.5\mbox{ to }10)100$ (but in a different notation). Also, eigenvalues for large values of $q$. Precision is generally 8D.

• ##### 4: Bibliography N
• National Bureau of Standards (1967) Tables Relating to Mathieu Functions: Characteristic Values, Coefficients, and Joining Factors. 2nd edition, National Bureau of Standards Applied Mathematics Series, U.S. Government Printing Office, Washington, D.C..
• ##### 5: 23.20 Mathematical Applications
The addition law states that to find the sum of two points, take the third intersection with $C$ of the chord joining them (or the tangent if they coincide); then its reflection in the $x$-axis gives the required sum. …
###### §23.20(iii) Factorization
§27.16 describes the use of primality testing and factorization in cryptography. …