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

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=9/2, b₁>=-11/2

For fixed z and a₁=4, a₂=9/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{4, 9/2}, {-(11/2), -(9/2)}, -z] == (1/3094331625) (3094331625 - 2250423000 z + 1964655000 z^2 - 2918916000 z^3 + 10216206000 z^4 - 185253868800 z^5 - 10559470521600 z^6 + 139175438976000 z^7 - 360012424262400 z^8 + 373421896243200 z^9 - 197707265095680 z^10 + 60164879523840 z^11 - 11232358502400 z^12 + 1331568967680 z^13 - 101423677440 z^14 + 4911980544 z^15 - 145231872 z^16 + 2375680 z^17 - 16384 z^18) + (1/3094331625) ((2048 Sqrt[Pi] (17581536000 z^(13/2) - 117796291200 z^(15/2) + 239729414400 z^(17/2) - 220603824000 z^(19/2) + 109111665600 z^(21/2) - 31846802400 z^(23/2) + 5787573120 z^(25/2) - 673826040 z^(27/2) + 50688450 z^(29/2) - 2433315 z^(31/2) + 71490 z^(33/2) - 1164 z^(35/2) + 8 z^(37/2)) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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</apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 117796291200 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 17581536000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </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> </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]