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

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=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=6, b₁>=-11/2

For fixed z and a₁=1/2, a₂=6, b₁=-7/2

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

Input Form

HypergeometricPFQ[{1/2, 6}, {-(7/2), 7/2}, z] == (-16200 + 18000 z - 10440 z^2 + 3780 z^3 - 741 z^4 - 280 z^5 + 1440 z^6 + 320 z^7 + 16 z^8)/(6720 z^2) + (1/(13440 z^(5/2))) (E^z Sqrt[Pi] (16200 - 28800 z + 32040 z^2 - 20340 z^3 + 8445 z^4 - 2550 z^5 + 600 z^6 + 3184 z^7 + 656 z^8 + 32 z^9) 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]