Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ajg4)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=5, b₁>=-11/2

For fixed z and a₁=5/2, a₂=5, b₁=-11/2

http://functions.wolfram.com/07.25.03.ajg4.01

Input Form

HypergeometricPFQ[{5/2, 5}, {-(11/2), -(1/2)}, -z] == (1/93555) (93555 - 425250 z - 1984500 z^2 - 3969000 z^3 - 6985440 z^4 - 15567552 z^5 - 86486400 z^6 + 146586240 z^7 - 76093632 z^8 + 18207168 z^9 - 2265144 z^10 + 149904 z^11 - 4960 z^12 + 64 z^13) - (1/93555) ((4 Sqrt[Pi] (-34186320 z^(13/2) + 44442216 z^(15/2) - 21057624 z^(17/2) + 4817673 z^(19/2) - 584424 z^(21/2) + 38088 z^(23/2) - 1248 z^(25/2) + 16 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]