Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an8n)

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=5, b₁>=-11/2

For fixed z and a₁=5, a₂=5, b₁=-5/2

http://functions.wolfram.com/07.25.03.an8n.01

Input Form

HypergeometricPFQ[{5, 5}, {-(5/2), 2}, z] == (1/69120) (69120 - 345600 z + 1382400 z^2 - 11289600 z^3 - 30844215 z^4 - 22977792 z^5 - 7434780 z^6 - 1201920 z^7 - 100368 z^8 - 4096 z^9 - 64 z^10) + (1/138240) (E^z Sqrt[Pi] (-41409225 z^(7/2) - 79472250 z^(9/2) - 52404300 z^(11/2) - 15980760 z^(13/2) - 2500272 z^(15/2) - 204768 z^(17/2) - 8256 z^(19/2) - 128 z^(21/2)) Erf[Sqrt[z]])

Standard Form

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MathML Form

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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]