Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.am9t)

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=11/2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.am9t.01

Input Form

HypergeometricPFQ[{4, 11/2}, {-(11/2), -(9/2)}, -z] == (1/27848984625) (27848984625 - 24754653000 z + 25540515000 z^2 - 43783740000 z^3 + 173675502000 z^4 - 3519823507200 z^5 - 221748880953600 z^6 + 3273049067904000 z^7 - 9482804215315200 z^8 + 11064322879948800 z^9 - 6637103950878720 z^10 + 2312032647536640 z^11 - 501112333209600 z^12 + 70310813368320 z^13 - 6512667525120 z^14 + 399187132416 z^15 - 15921364992 z^16 + 394977280 z^17 - 5505024 z^18 + 32768 z^19) - (1/27848984625) ((4096 Sqrt[Pi] (-193396896000 z^(13/2) + 1431137030400 z^(15/2) - 3234278678400 z^(17/2) + 3328182950400 z^(19/2) - 1857278808000 z^(21/2) + 618660504000 z^(23/2) - 130235545440 z^(25/2) + 17916441840 z^(27/2) - 1636906590 z^(29/2) + 99354750 z^(31/2) - 3934605 z^(33/2) + 97098 z^(35/2) - 1348 z^(37/2) + 8 z^(39/2)) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]