Threefold Introduction to Fractional Derivatives

Sie sind hier: ICP » R. Hilfer » Publikationen

Appendix A Tables

[page 59, §1]

[59.1.1] Let α∈C, x>a


	f⁢x		Ia+α⁢f⁢x


	f⁢λ⁢x		λ-α⁢Iλ⁢a+α⁢f⁢λ⁢x,λ>0		(A.1)
					(A.2)
	x-aβ		Γ⁢β+1Γ⁢α+β+1⁢x-aα+β		(A.3)
			Re⁢β>0
					(A.4)
	eλ⁢x		eλ⁢a⁢x-aα⁢E1,α+1⁢λ⁢x-a		(A.5)
			λ∈R
					(A.6)
	x-aβ-1⁢eλ⁢x		Γ⁢β⁢eλ⁢aΓ⁢α+β⁢x-a1α+β-1⁢F1⁢β;α+β;λ⁢x-a		(A.7)
			Re⁢β>0
					(A.8)
	x-aβ-1⁢log⁡x-a		Γ⁢β⁢x-aα+β-1Γ⁢α+β⁢ψ⁢β-ψ⁢α+β+log⁡x-a		(A.9)
					(A.10)
	x-aβ-1⁢Eγ,β⁢x-aγ		x-aα+β-1⁢Eγ,α+β⁢x-aγ		(A.11)
			Re⁢β>0,Re⁢γ>0

Table A.1: Some fractional integrals