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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=4, b₁>=-11/2

For fixed z and a₁=3/2, a₂=4, b₁=-11/2

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

Input Form

HypergeometricPFQ[{3/2, 4}, {-(11/2), -(5/2)}, z] == (1/467775) (467775 + 204120 z + 189000 z^2 + 756000 z^3 - 4762800 z^4 + 18627840 z^5 - 145297152 z^6 - 368640000 z^7 - 255310080 z^8 - 76958208 z^9 - 11619840 z^10 - 908672 z^11 - 34816 z^12 - 512 z^13) - (1/467775) (64 E^z Sqrt[Pi] (4069800 z^(13/2) + 7325640 z^(15/2) + 4515084 z^(17/2) + 1286796 z^(19/2) + 188397 z^(21/2) + 14466 z^(23/2) + 548 z^(25/2) + 8 z^(27/2)) Erf[Sqrt[z]])

Standard Form

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MathML Form

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<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]