Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4505)

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=-9/2, a₂>=-9/2

For fixed z and a₁=-9/2, a₂=3, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=3, b₁=3/2

http://functions.wolfram.com/07.25.03.4505.01

Input Form

HypergeometricPFQ[{-(9/2), 3}, {3/2, 6}, z] == (12 (420 + 570 z + 323 z^2))/(46189 z^5) + (1/(5542680 z^5)) (E^z (-604800 - 216000 z + 53280 z^2 + 155520 z^3 - 120960 z^4 + 3512535 z^5 - 3036660 z^6 + 778056 z^7 - 74096 z^8 + 2288 z^9)) + (1/(11085360 Sqrt[z])) (Sqrt[Pi] (2078505 - 9447750 z + 6783000 z^2 - 1627920 z^3 + 150480 z^4 - 4576 z^5) Erfi[Sqrt[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]