Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ahu3)

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=2, a₂>=2

For fixed z and a₁=2, a₂=7/2, b₁>=-11/2

For fixed z and a₁=2, a₂=7/2, b₁=-7/2

http://functions.wolfram.com/07.25.03.ahu3.01

Input Form

HypergeometricPFQ[{2, 7/2}, {-(7/2), -(5/2)}, z] == (1/23625) (23625 + 18900 z + 34020 z^2 + 332640 z^3 - 10810800 z^4 - 72959040 z^5 - 93616320 z^6 - 44971008 z^7 - 9920256 z^8 - 1070080 z^9 - 54272 z^10 - 1024 z^11) - (1/23625) (512 E^z Sqrt[Pi] (55440 z^(9/2) + 206640 z^(11/2) + 219240 z^(13/2) + 96600 z^(15/2) + 20370 z^(17/2) + 2142 z^(19/2) + 107 z^(21/2) + 2 z^(23/2)) Erf[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]