Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an30)

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=6, b₁>=-11/2

For fixed z and a₁=9/2, a₂=6, b₁=-7/2

http://functions.wolfram.com/07.25.03.an30.01

Input Form

HypergeometricPFQ[{9/2, 6}, {-(7/2), 11/2}, -z] == (1/(2800 z^4)) (-4233600 - 1411200 z - 423360 z^2 - 100800 z^3 - 16800 z^4 + 720 z^5 + 4200 z^6 + 7112 z^7 + 28455 z^8 - 24880 z^9 + 6032 z^10 - 544 z^11 + 16 z^12) + (1/(5600 z^(9/2))) ((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 - 76970 z^9 + 55288 z^10 - 12592 z^11 + 1104 z^12 - 32 z^13) Erfi[Sqrt[z]])/E^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]