\ \ \
\left( \mathtt{ii}\right) $ $_{q}L\left( _{q}\cos ax\right) \left( v\right) =\dfrac{q^{2}v}{q^{2}v^{2}+a^{2}},$ $\left\vert a\right\vert <qv.$

$\left( \mathtt{iii}\right) $ $_{q}S\left( _{q}\sin ax\right) \left(
u\right) =-\dfrac{qa}{q^{2}+a^{2}u^{2}},$ $\left\vert au\right\vert <qv;$ $\left( \mathtt{iv}\right) $ $_{q}S\left( _{q}\cos ax\right) \left( u\right) =\dfrac{q^{2}}{q^{2}+a^{2}u^{2}},$ $\left\vert au\right\vert <qv.$

Further results concerning some other special functions can be obtained similarly.

$q$-Analogues of $N$-Transforms for the $q$-Fox’s $H$-Function
==============================================================

Let $\alpha _{j}$ and $\beta _{j}$ be positive integers and $0\leq
m\leq N;$ $0\leq n\leq M.$ Due to $\left[ 27\right] ,$ the $q$-analogue of the Fox’s $H$-function is given as

$H_{M,N}^{m,n}\left[ x;q\left\vert 
\begin{array}{c}
\left( a_{1},\alpha _{1}\right) ,\left( a_{2},\alpha _{2}\right) ,...,\left(
a_{\mu },\alpha _{M}\right) \\ 
\left( b_{1},\beta _{1}\right) ,\left( b_{2},\beta _{2}\right) ,...,\left(
b_{N},\beta _{N}\right)\end{array}\right. \right] =$

$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \dfrac{1}{2\pi i}\dint\nolimits_{C}\dfrac{\dprod\limits_{j=1}^{m}G\left( q^{b_{j}-\beta
_{j}s}\right) \dprod\limits_{j=1}^{n}G\left( q^{1-a_{j}+\alpha _{j}s}\right)
\pi x^{s}}{\dprod\limits_{j=m+1}^{N}G\left( q^{1-b_{j}+\beta _{j}s}\right)
\dprod\limits_{j=n+1}^{M}G\left( q^{a_{j}-\alpha _{j}s}\right) G\left(
q^{1-s}\right) \sin \pi s}d_{q}s$$$\tag{45}$$where $G$ is defined in terms of the product$$G\left( q^{^{\alpha }}\right) =\dprod\limits_{0}^{\infty }\left( 1-q^{\alpha
-k}\right) ^{-1}=\frac{1}{\left( q^{^{\alpha }},q\right) _{\infty }}. 
\tag{46}$$

The contour $C$ is parallel to $\func{Re}\left( ws\right) =0,$ with indentations in such away all poles of $G\left( q^{b_{j}-\beta
_{j}s}\right) 