Different types of sinc integrals are investigated when the standard sine function is replaced by the generalised sinp,q in two parameters. A striking generalisation of the improper Dirichlet integral is achieved. A second surprising but interesting generalisation of the identity between the Dirichlet integral and that of the integrand sinc2 is discovered. Moreover, an asymptotically sharpened form of Ball's integral inequality is obtained in terms of two parameters.
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