Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aj4y)

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=4, b₁>=-11/2

For fixed z and a₁=5/2, a₂=4, b₁=-11/2

http://functions.wolfram.com/07.25.03.aj4y.01

Input Form

HypergeometricPFQ[{5/2, 4}, {-(11/2), 7/2}, z] == (1/(6237 z^2)) (-483840 + 161280 z - 42147 z^2 + 8280 z^3 - 840 z^4 - 288 z^5 + 336 z^6 - 352 z^7 + 948 z^8 + 272 z^9 + 16 z^10) + (1/(6237 z^(5/2))) (2 E^z Sqrt[Pi] (120960 - 120960 z + 60480 z^2 - 20160 z^3 + 5040 z^4 - 1008 z^5 + 168 z^6 - 24 z^7 + 3 z^8 + 538 z^9 + 140 z^10 + 8 z^11) 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]