Definite integrals from 0 to Infinity over a product of two hypergeometric (including exponential, trigonometric, hyperbolic, Bessel, etc) functions (optionally times a power of the integration variable) always result in a hygergeometric function (HypergeometricPFQ or MeijerG). With some experience, many important properties such as the asymptotic behavior at small or large argument can be immediately seen from the hypergeometric notation.

Unfortunately, Mathematica takes this nice, compact and very informative output and "simplifies" it into a combination of simpler functions, often resulting in rather lengthy outputs where all the useful information contained in the original hypergeometric notation is lost.

How can I prevent this simplification?
Integrate should result in a HypergeometricPFQ or MeijerG without further simplification unless explicitly requested via Simplify or FullSimplify.


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