Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ajum)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=6, b₁>=-11/2

For fixed z and a₁=5/2, a₂=6, b₁=-3/2

http://functions.wolfram.com/07.25.03.ajum.01

Input Form

HypergeometricPFQ[{5/2, 6}, {-(3/2), 7/2}, -z] == (-1080 - 360 z + 468 z^2 + 1620 z^3 + 8955 z^4 - 12072 z^5 + 3936 z^6 - 448 z^7 + 16 z^8)/(576 z^2) + (1/(1152 z^(5/2))) ((Sqrt[Pi] (1080 + 1080 z + 540 z^2 + 180 z^3 + 45 z^4 - 27018 z^5 + 27672 z^6 - 8304 z^7 + 912 z^8 - 32 z^9) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]