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

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, a₂>=5

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

For fixed z and a₁=5, a₂=11/2, b₁=-9/2

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

Input Form

HypergeometricPFQ[{5, 11/2}, {-(9/2), 5/2}, -z] == (1/893025) (893025 + 2182950 z + 3474900 z^2 + 5405400 z^3 + 11138400 z^4 + 58605120 z^5 - 92093760 z^6 + 45191880 z^7 - 10328760 z^8 + 1236300 z^9 - 79144 z^10 + 2544 z^11 - 32 z^12) + (1/893025) ((2 Sqrt[Pi] z^(11/2) (-45349200 + 55378350 z - 24912990 z^2 + 5455185 z^3 - 637320 z^4 + 40200 z^5 - 1280 z^6 + 16 z^7) 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]