Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ajr9)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=6, b₁>=-11/2

For fixed z and a₁=5/2, a₂=6, b₁=-11/2

http://functions.wolfram.com/07.25.03.ajr9.01

Input Form

HypergeometricPFQ[{5/2, 6}, {-(11/2), -(11/2)}, -z] == (1/4862521125) (4862521125 - 2411167500 z + 1458607500 z^2 - 1428840000 z^3 + 2829103200 z^4 - 16345929600 z^5 + 899026128000 z^6 - 40323036902400 z^7 + 182390463763200 z^8 - 279424854696960 z^9 + 203118614737920 z^10 - 81895384166400 z^11 + 19946506567680 z^12 - 3081153761280 z^13 + 309517787136 z^14 - 20340745344 z^15 + 862041600 z^16 - 22559744 z^17 + 329728 z^18 - 2048 z^19) + (1/4862521125) ((64 Sqrt[Pi] (-94354243200 z^(13/2) + 1320959404800 z^(15/2) - 4251491193600 z^(17/2) + 5555702476800 z^(19/2) - 3701081008800 z^(21/2) + 1416207723840 z^(23/2) - 333659702880 z^(25/2) + 50417539200 z^(27/2) - 4988810295 z^(29/2) + 324388890 z^(31/2) - 13643112 z^(33/2) + 355056 z^(35/2) - 5168 z^(37/2) + 32 z^(39/2)) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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<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]