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

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=5, b₁>=-11/2

For fixed z and a₁=9/2, a₂=5, b₁=-11/2

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

Input Form

HypergeometricPFQ[{9/2, 5}, {-(11/2), -(9/2)}, -z] == (1/3094331625) (3094331625 - 2813028750 z + 2946982500 z^2 - 5108103000 z^3 + 20432412000 z^4 - 416821204800 z^5 - 26398676304000 z^6 + 391734203616000 z^7 - 1140348973881600 z^8 + 1336362622963200 z^9 - 804924585722880 z^10 + 281483471001600 z^11 - 61234996838400 z^12 + 8622405550080 z^13 - 801405480960 z^14 + 49284393984 z^15 - 1972016640 z^16 + 49075200 z^17 - 686080 z^18 + 4096 z^19) - (1/3094331625) ((256 Sqrt[Pi] (-369212256000 z^(13/2) + 2744477769600 z^(15/2) - 6228827942400 z^(17/2) + 6435762076800 z^(19/2) - 3605445950400 z^(21/2) + 1205474205600 z^(23/2) - 254683517760 z^(25/2) + 35159057640 z^(27/2) - 3223124730 z^(29/2) + 196276185 z^(31/2) - 7797720 z^(33/2) + 193032 z^(35/2) - 2688 z^(37/2) + 16 z^(39/2)) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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</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]