I am trying to find an analytical form (if any) of the following integral: $$ \xi_{n,m}(a,b,c) =\int_0^\infty k^n\, j_1(ak)\, j_1(bk)\, j_m(ck)\mathrm{d}k, $$ where $a$, $b$ and $c>0$ and $j_n$ is the n-th spherical Bessel function.
I have found this link http://functions.wolfram.com/Bessel-TypeFunctions/SphericalBesselJ/21/02/02/0005/ that seem to give a solution in the range of my problem. However, I don't understand how to read this formula.
I have already tried unsuccessfully to solve it using a symbolic computation program (Mathematica) but the answer didn't come out.
Can anyone decipher the formula given in the link above or has anyone a knowledge about this integral?
UPDATE: the answer seem to come from $$ \int_0^\infty t^{\alpha-1}j_\lambda(a t) j_\mu(b t) j_\nu(c t)\mathrm{d}t = \frac{2^ {\alpha-4}b^\mu c^{-\alpha-\lambda-\mu}\pi^{3/2}\Gamma\left[\frac{\alpha+\lambda+\mu+\nu}{2}\right]}{\Gamma[\lambda +3/2]\Gamma[\mu+3/2]\Gamma\left[\frac{3-\alpha-\lambda-\mu+\nu}{2}\right]}F_{0,1,1}^ {2,0,0} \left( \begin{matrix} \frac{\alpha+\lambda+\mu+\nu}{2},\frac{\alpha+\lambda+\mu-\nu-1}{2};;;\\ ;\lambda +\frac{3}{2};\mu+\frac{3}{2}; \end{matrix}\ \ \ \frac{a^2}{c^2}, \frac{b^2}{c^2} \right) $$ My issue being now that I don't understand the $F_{0,1,1}^ {2,0,0}$ notation.