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

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=-7/2

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

Input Form

HypergeometricPFQ[{5, 11/2}, {-(7/2), -(1/2)}, -z] == (1/297675) (297675 - 4677750 z - 72972900 z^2 - 567567000 z^3 - 7718911200 z^4 + 40138338240 z^5 - 54934588800 z^6 + 33509790720 z^7 - 10897908480 z^8 + 2056080000 z^9 - 233888928 z^10 + 16133040 z^11 - 654752 z^12 + 14272 z^13 - 128 z^14) + (1/297675) ((8 Sqrt[Pi] (2205403200 z^(9/2) - 7317928800 z^(11/2) + 8501598000 z^(13/2) - 4770148320 z^(15/2) + 1478305080 z^(17/2) - 270714150 z^(19/2) + 30205665 z^(21/2) - 2056680 z^(23/2) + 82728 z^(25/2) - 1792 z^(27/2) + 16 z^(29/2)) 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]