ToDistribution

Description

ToDistribution[exp,x] replaces (1-x)^(a Epsilon - 1) in exp by 1/(a Epsilon) DeltaFunction[1-x] + 1/(1-x) + a Epsilon Log[1-x]/(1-x) + 1/2 a^2 Epsilon^2 Log[1-x]^2/(1-x)] and (1-x)^(a Epsilon - 2) in exp by -1/(a Epsilon) DeltaFunctionPrime[1-x] + 1/(1-x)^2 + (a Epsilon) Log[1-x]/(1-x)^2 + a^2 Epsilon^2/2 Log[1-x]^2/(1-x)^2 + a^3 Epsilon^3/6 Log[1-x]^3/(1-x)^2.

Options[ToDistribution]

See also:  PlusDistribution.

Examples

SetOptions[ToDistribution, 
      PlusDistribution -> PlusDistribution]

ToDistribution[(1 - x)^(Epsilon - 1), x]

SetOptions[ToDistribution, 
      PlusDistribution -> Identity]

ToDistribution[(1 - x)^(Epsilon - 2), x]

Series2[
      Integrate[(((1 - x))^(Epsilon - 2)), {x, 0, 1}, 
        GenerateConditions -> False], Epsilon, 3]

Options@Integrate

Integrate2[
      ToDistribution[(1 - x)^(Epsilon - 2), x], {x, 0, 1}]