q-derivatives

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1: 17.2 Calculus

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§17.2(iv) Derivatives

►The $q$-derivatives of $f(z)$ are defined by … ►When $q\to 1$ the $q$-derivatives converge to the corresponding ordinary derivatives. …

2: 23.15 Definitions

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23.15.8 $${\theta }_1^{\prime }(0,q)={\partial {\theta }_1(z,q)/\partial z|}_{z=0}.$$

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Symbols:

${\theta }_j(z,q)$: theta function, $\frac{\partial f}{\partial x}$: partial derivative of $f$ with respect to $x$ , $\partial x$: partial differential of $x$ , $q$: nome and $z$: complex

Permalink:

http://dlmf.nist.gov/23.15.E8

Encodings:

pMML, png, TeX

See also:

Annotations for §23.15(ii), §23.15(ii), §23.15 and Ch.23

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3: 18.27 $q$-Hahn Class

… ►In the $q$-Hahn class OP’s the role of the operator $d/dx$ in the Jacobi, Laguerre, and Hermite cases is played by the $q$-derivative ${𝒟}_q$, as defined in (17.2.41). …

4: 36.2 Catastrophes and Canonical Integrals

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$$\frac{{\partial }^{2q+1}}{{\partial x_1}^{2q+1}}{\mathrm{\Psi }}_K\left(\mathbf{0}\right)=0,$$ $K$ even,

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