## A note on dual integral equations involving inverse associated Weber-Orr transforms.(English)Zbl 0853.45003

C. Nasim [Int. J. Math. Math. Sci. 14, No. 1, 163-176 (1991; Zbl 0721.45001)] solved similar dual integral equations with a different set of conditions on the parameters involved. The similarity of the system is striking. The authors solve $W^{-1}_{\nu - \gamma, \nu} \bigl[ \xi^{- 2 \alpha} \Psi (\xi), x \bigr] = g_1 (x), \quad a \leq x \leq c,$
$W^{-1}_{\nu - \gamma, \nu} \bigl[ \xi^{- 2 \beta} \Psi (\xi), x \bigr] = g_2 (x), \quad c < x < \infty,$ where $$\nu > - {1 \over 2}$$, $$\gamma (> 0)$$ is not an integer with $$\gamma + \alpha - \beta$$ a positive integer, $$\Psi$$ an unknown function. The method of Noble is used to reduce the above pair to a Fredholm integral equation of second kind for $$- 1 < \alpha - \beta < 1$$, with $$\alpha - \beta \neq 0$$.

### MSC:

 45F10 Dual, triple, etc., integral and series equations 44A20 Integral transforms of special functions 45B05 Fredholm integral equations

Zbl 0721.45001
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