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

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=5, a₂>=5

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

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

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

Input Form

HypergeometricPFQ[{5, 11/2}, {-(9/2), -(7/2)}, z] == (1/281302875) (281302875 + 491163750 z + 1094593500 z^2 + 5108103000 z^3 + 115783668000 z^4 - 7919602891200 z^5 - 126279382320000 z^6 - 390168274809600 z^7 - 481470363360000 z^8 - 303608660313600 z^9 - 110659295738880 z^10 - 25001319168000 z^11 - 3645418291200 z^12 - 349990901760 z^13 - 22186206720 z^14 - 913392384 z^15 - 23349760 z^16 - 334848 z^17 - 2048 z^18) - (1/281302875) (128 E^z Sqrt[Pi] (228559968000 z^(11/2) + 1802107440000 z^(13/2) + 4310992627200 z^(15/2) + 4670931484800 z^(17/2) + 2732552625600 z^(19/2) + 950699786400 z^(21/2) + 208382932800 z^(23/2) + 29768449320 z^(25/2) + 2817617130 z^(27/2) + 176809665 z^(29/2) + 7225800 z^(31/2) + 183720 z^(33/2) + 2624 z^(35/2) + 16 z^(37/2)) Erf[Sqrt[z]])

Standard Form

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MathML Form

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</cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1802107440000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 228559968000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <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> </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]