The PDF of Stable Distribution in terms of a Fox H-function for the case $α≤1$ is available at https://reference.wolfram.com/language/ref/FoxH.html (Examples\Applications) in the form:
$S(x;\alpha,\beta,\mu,\sigma)=\frac{1}{\alpha A}H^{1,1}_{2,2} \left[ \frac{|x-\mu|}{A} \Bigg| \begin{matrix} (1-\frac {1}{\alpha},\frac {1}{\alpha}), & (\frac{1-B}{2},\frac{1+B}{2}) \\ (0,1), & (\frac{1-B}{2},\frac{1+B}{2}) \end{matrix}\right]$
where
$A=\sigma(1+\beta^2\tan^2(\pi\alpha/2))^\frac{1}{2\alpha}$
and
$B=\frac{2}{\pi\alpha}{\rm sign}(x-\mu)\arctan(\beta\tan(\pi\alpha/2)).$
I checked it numerically that the above formula really gives $S(x;\alpha,\beta,\mu,\sigma)$ for the case $0<\alpha<1$. For the case $1<\alpha<2$, however, the above formula gives completely wrong results.
For more complex physics-related calculations I need the PDF of StableDistribution in terms of FoxH for the case $1<\alpha<2$.
I found two sources:
[1] Ralf Metzler, Joseph Klafter, The random walk's guide to anomalous diffusion: a fractional dynamics approach, Physics Reports, Volume 339, Issue 1, December 2000, Pages 1-77 https://doi.org/10.1016/S0370-1573(00)00070-3 (relevant part: formulas (C.17) and (C.18) in Appendix C)
[2] A.M. Mathai, Ram Kishore Saxena, and Hans J. Haubold, The H-Function: Theory and Applications (Springer; 2010th edition) (relevant part: formulas (6.168) and (6.169))
The relevant formulas in the above sources seem not to be sufficient to get $S(x;\alpha,\beta,\mu,\sigma)$ in terms of a Fox H-function for the case $1<\alpha<2$.
Could you please help me to find $S(x;\alpha,\beta,\mu,\sigma)$ in terms of a Fox H-function for the case $1<\alpha<2$?
