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

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.ampi.01

Input Form

HypergeometricPFQ[{9/2, 5}, {-(11/2), -(11/2)}, z] == (1/34037647875) (34037647875 + 25317258750 z + 20628877500 z^2 + 25540515000 z^3 + 61297236000 z^4 + 416821204800 z^5 + 26398676304000 z^6 + 1364239285920000 z^7 + 7106917487443200 z^8 + 12543698267251200 z^9 + 10539431454827520 z^10 + 4942306507622400 z^11 + 1413257752166400 z^12 + 259734044344320 z^13 + 31625330688000 z^14 + 2586643347456 z^15 + 141905756160 z^16 + 5121162240 z^17 + 115984384 z^18 + 1486848 z^19 + 8192 z^20) + (1/34037647875) (512 E^z Sqrt[Pi] (369212256000 z^(13/2) + 5858167795200 z^(15/2) + 21430961596800 z^(17/2) + 31971876249600 z^(19/2) + 24462991828800 z^(21/2) + 10838291184000 z^(23/2) + 2988258829920 z^(25/2) + 535955978880 z^(27/2) + 64167180210 z^(29/2) + 5185886580 z^(31/2) + 282051105 z^(33/2) + 10114104 z^(35/2) + 227976 z^(37/2) + 2912 z^(39/2) + 16 z^(41/2)) Erf[Sqrt[z]])

Standard Form

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MathML Form

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<times /> <cn type='integer'> 21430961596800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5858167795200 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 369212256000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> Erf </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]