Obtain Simple Differences and Ratios for Special Functions 

Obtain simple differences and ratios for Beta and GammaRegularized.

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X DifferenceDelta[Beta[z, n, m], n]

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X DiscreteRatio[Beta[z, n, m], n]

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X DifferenceDelta[GammaRegularized[n, z], n]

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X DiscreteRatio[GammaRegularized[n, z], n]

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Create a gallery of elegant differences and ratios.

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X diffratios = Inactivate[{DifferenceDelta[Gamma[n, z], n] , DifferenceDelta[GammaRegularized[n, z], n], DifferenceDelta[Beta[z, n, m], m] , DifferenceDelta[MarcumQ[n, a, z], n], DiscreteRatio[Gamma[n, z], n] , DiscreteRatio[GammaRegularized[n, z], n], DiscreteRatio[Beta[z, n, m], m], DiscreteRatio[MarcumQ[n, a, z], n]}, DifferenceDelta | DiscreteRatio]; FormulaGallery[forms_List] := Module[{vals = ParallelMap[Activate, forms]}, Column[Table[ Style[forms[[r]] == vals[[r]], ScriptLevel -> 0], {r, Length[forms]}], Dividers -> All, Alignment -> "\[LongEqual]", Background -> LightOrange, Spacings -> 1]]; FormulaGallery[diffratios] // TraditionalForm

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