Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ant0)

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=-7/2

http://functions.wolfram.com/07.25.03.ant0.01

Input Form

HypergeometricPFQ[{11/2, 6}, {-(7/2), -(5/2)}, z] == (1/22325625) (22325625 + 84199500 z + 510810300 z^2 + 13621608000 z^3 - 1042053012000 z^4 - 18353365430400 z^5 - 61398826070400 z^6 - 81018530933760 z^7 - 54150293664000 z^8 - 20781544089600 z^9 - 4918370042880 z^10 - 748129213440 z^11 - 74674880256 z^12 - 4907291040 z^13 - 208924800 z^14 - 5511424 z^15 - 81408 z^16 - 512 z^17) - (1/22325625) (16 E^z Sqrt[Pi] (251415964800 z^(9/2) + 2148463699200 z^(11/2) + 5510053382400 z^(13/2) + 6347520547200 z^(15/2) + 3922345879200 z^(17/2) + 1433830325760 z^(19/2) + 328773543840 z^(21/2) + 48953150280 z^(23/2) + 4814411715 z^(25/2) + 313068570 z^(27/2) + 13227528 z^(29/2) + 346992 z^(31/2) + 5104 z^(33/2) + 32 z^(35/2)) Erf[Sqrt[z]])

Standard Form

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MathML Form

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type='integer'> 251415964800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <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]