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

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=6, b₁>=-11/2

For fixed z and a₁=7/2, a₂=6, b₁=-7/2

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

Input Form

HypergeometricPFQ[{7/2, 6}, {-(7/2), 11/2}, z] == (1/(800 z^4)) (4233600 - 1638000 z + 498960 z^2 - 123480 z^3 + 25800 z^4 - 5130 z^5 + 1470 z^6 - 1183 z^7 + 3804 z^8 + 2360 z^9 + 368 z^10 + 16 z^11) + (1/(1600 z^(9/2))) (E^z Sqrt[Pi] (-4233600 + 4460400 z - 2343600 z^2 + 819000 z^3 - 214200 z^4 + 44730 z^5 - 7770 z^6 + 1155 z^7 - 150 z^8 + 9640 z^9 + 5072 z^10 + 752 z^11 + 32 z^12) 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]