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

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=-11/2

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

Input Form

HypergeometricPFQ[{11/2, 6}, {-(11/2), -(5/2)}, -z] == (1/2210236875) (2210236875 - 5304568500 z + 17878360500 z^2 - 204324120000 z^3 - 3126159036000 z^4 - 26398676304000 z^5 - 406539615081600 z^6 + 2587031598412800 z^7 - 4482230927328000 z^8 + 3598204614681600 z^9 - 1609717608576000 z^10 + 440724946636800 z^11 - 77898630297600 z^12 + 9160257254400 z^13 - 726241858560 z^14 + 38743401600 z^15 - 1363342848 z^16 + 30178304 z^17 - 378880 z^18 + 2048 z^19) - (1/2210236875) ((64 Sqrt[Pi] (-15568450128000 z^(13/2) + 62273800512000 z^(15/2) - 90663327216000 z^(17/2) + 66402894096000 z^(19/2) - 28123855452000 z^(21/2) + 7435145163600 z^(23/2) - 1283724703800 z^(25/2) + 148524674760 z^(27/2) - 11640123495 z^(29/2) + 615788250 z^(31/2) - 21535080 z^(33/2) + 474480 z^(35/2) - 5936 z^(37/2) + 32 z^(39/2)) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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type='integer'> 15568450128000 </cn> <apply> <power /> <ci> 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]