Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aj54)

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.aj54.01

Input Form

HypergeometricPFQ[{5/2, 4}, {-(11/2), 11/2}, z] == (1/(99 z^4)) (190512000 - 58060800 z + 17176320 z^2 - 3971520 z^3 + 746451 z^4 - 117720 z^5 + 15960 z^6 - 1896 z^7 + 201 z^8 - 20 z^9 + 4 z^10) + (1/(198 z^(9/2))) (E^z Sqrt[Pi] (-190512000 + 185068800 z - 89752320 z^2 + 28969920 z^3 - 7000560 z^4 + 1350720 z^5 - 216720 z^6 + 29736 z^7 - 3561 z^8 + 378 z^9 - 36 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]