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

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=11/2, a₂>=11/2

For fixed z and a₁=11/2, a₂=6, b₁>=-11/2

For fixed z and a₁=11/2, a₂=6, b₁=-9/2

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

Input Form

HypergeometricPFQ[{11/2, 6}, {-(9/2), -(1/2)}, -z] == (1/13395375) (13395375 - 196465500 z - 2554051500 z^2 - 13621608000 z^3 - 69470200800 z^4 - 754247894400 z^5 + 3253170211200 z^6 - 4032032256000 z^7 + 2348893209600 z^8 - 761140316160 z^9 + 148873082400 z^10 - 18319492800 z^11 + 1440017520 z^12 - 71688960 z^13 + 2172672 z^14 - 36352 z^15 + 256 z^16) - (1/13395375) ((8 Sqrt[Pi] (-199989972000 z^(11/2) + 578432534400 z^(13/2) - 618943323600 z^(15/2) + 334075039200 z^(17/2) - 103491136350 z^(19/2) + 19674144000 z^(21/2) - 2375776305 z^(23/2) + 184352490 z^(25/2) - 9094680 z^(27/2) + 273840 z^(29/2) - 4560 z^(31/2) + 32 z^(33/2)) 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]