Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ane3)

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=-5/2

http://functions.wolfram.com/07.25.03.ane3.01

Input Form

HypergeometricPFQ[{5, 11/2}, {-(5/2), -(3/2)}, -z] == (1/127575) (127575 - 935550 z + 24324300 z^2 + 1702701000 z^3 - 26140514400 z^4 + 74283168960 z^5 - 81276773760 z^6 + 43895208960 z^7 - 13205214720 z^8 + 2358656640 z^9 - 257561472 z^10 + 17208816 z^11 - 680736 z^12 + 14528 z^13 - 128 z^14) + (1/127575) ((8 Sqrt[Pi] (-778377600 z^(7/2) + 5837832000 z^(9/2) - 12819643200 z^(11/2) + 12335425200 z^(13/2) - 6196765680 z^(15/2) + 1784303640 z^(17/2) - 309952440 z^(19/2) + 33230385 z^(21/2) - 2192760 z^(23/2) + 85992 z^(25/2) - 1824 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]