Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ak1l)

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=3, a₂>=3

For fixed z and a₁=3, a₂=7/2, b₁>=-11/2

For fixed z and a₁=3, a₂=7/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.ak1l.01

Input Form

HypergeometricPFQ[{3, 7/2}, {-(9/2), -(5/2)}, z] == (1/212625) (212625 + 198450 z + 340200 z^2 + 2494800 z^3 - 32432400 z^4 + 454053600 z^5 + 2103978240 z^6 + 2352407040 z^7 + 1102429440 z^8 + 258869760 z^9 + 32655360 z^10 + 2224128 z^11 + 76288 z^12 + 1024 z^13) + (1/212625) (256 E^z Sqrt[Pi] (3931200 z^(11/2) + 11491200 z^(13/2) + 10962000 z^(15/2) + 4757760 z^(17/2) + 1071000 z^(19/2) + 131760 z^(21/2) + 8835 z^(23/2) + 300 z^(25/2) + 4 z^(27/2)) 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]