Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ak27)

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=3, a₂>=3

For fixed z and a₁=3, a₂=7/2, b₁>=-11/2

For fixed z and a₁=3, a₂=7/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.ak27.01

Input Form

HypergeometricPFQ[{3, 7/2}, {-(9/2), 11/2}, -z] == (1/(15 z^4)) (25401600 + 7257600 z + 2136960 z^2 + 483840 z^3 + 88815 z^4 + 13650 z^5 + 1800 z^6 + 208 z^7 + 22 z^8 + 4 z^9) + (1/(15 z^(9/2))) ((Sqrt[Pi] (-12700800 - 12096000 z - 5745600 z^2 - 1814400 z^3 - 428400 z^4 - 80640 z^5 - 12600 z^6 - 1680 z^7 - 195 z^8 - 20 z^9 - 4 z^10) 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]