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

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=5, b₁>=-11/2

For fixed z and a₁=9/2, a₂=5, b₁=-7/2

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

Input Form

HypergeometricPFQ[{9/2, 5}, {-(7/2), 11/2}, z] == (1/(280 z^4)) (-4233600 + 1411200 z - 423360 z^2 + 100800 z^3 - 19320 z^4 + 2880 z^5 - 120 z^6 - 392 z^7 + 1575 z^8 + 1042 z^9 + 172 z^10 + 8 z^11) + (1/(560 z^(9/2))) (E^z Sqrt[Pi] (4233600 - 4233600 z + 2116800 z^2 - 705600 z^3 + 176400 z^4 - 35280 z^5 + 5880 z^6 - 840 z^7 + 105 z^8 + 4040 z^9 + 2248 z^10 + 352 z^11 + 16 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]