# complex variable

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##### 2: 5.1 Special Notation
 $j,m,n$ nonnegative integers. … complex variable. real or complex variables with $|q|<1$. …
##### 3: 32.1 Special Notation
 $m,n$ integers. … complex variable. …
##### 4: 21.8 Abelian Functions
An Abelian function is a $2g$-fold periodic, meromorphic function of $g$ complex variables. In consequence, Abelian functions are generalizations of elliptic functions (§23.2(iii)) to more than one complex variable. …
##### 5: 4.34 Derivatives and Differential Equations
4.34.7 $\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}-a^{2}w=0,$
4.34.8 $\left(\frac{\mathrm{d}w}{\mathrm{d}z}\right)^{2}-a^{2}w^{2}=1,$
##### 6: 4.20 Derivatives and Differential Equations
4.20.9 $\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}+a^{2}w=0,$
4.20.10 $\left(\frac{\mathrm{d}w}{\mathrm{d}z}\right)^{2}+a^{2}w^{2}=1,$
4.20.12 $w=A\cos\left(az\right)+B\sin\left(az\right),$
##### 7: 6.1 Special Notation
 $x$ real variable. complex variable. …
##### 8: 25.1 Special Notation
 $k,m,n$ nonnegative integers. … complex variable. complex variable. …
##### 9: 4.14 Definitions and Periodicity
4.14.4 $\tan z=\frac{\sin z}{\cos z},$
4.14.5 $\csc z=\frac{1}{\sin z},$
4.14.6 $\sec z=\frac{1}{\cos z},$
##### 10: 4.28 Definitions and Periodicity
4.28.2 $\cosh z=\frac{e^{z}+e^{-z}}{2},$
4.28.5 $\operatorname{csch}z=\frac{1}{\sinh z},$