Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.alz5)

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=4, a₂>=4

For fixed z and a₁=4, a₂=9/2, b₁>=-11/2

For fixed z and a₁=4, a₂=9/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.alz5.01

Input Form

HypergeometricPFQ[{4, 9/2}, {-(11/2), 1/2}, -z] == (1/3274425) (3274425 + 21432600 z + 43659000 z^2 + 64864800 z^3 + 97297200 z^4 + 196035840 z^5 + 1015822080 z^6 - 1562803200 z^7 + 755354880 z^8 - 170580480 z^9 + 20216832 z^10 - 1283456 z^11 + 40960 z^12 - 512 z^13) + (1/3274425) ((64 Sqrt[Pi] (-24418800 z^(13/2) + 29302560 z^(15/2) - 12999420 z^(17/2) + 2814000 z^(19/2) - 325605 z^(21/2) + 20370 z^(23/2) - 644 z^(25/2) + 8 z^(27/2)) 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]