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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=6, b₁>=-11/2

For fixed z and a₁=3/2, a₂=6, b₁=-9/2

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

Input Form

HypergeometricPFQ[{3/2, 6}, {-(9/2), 11/2}, -z] == (1/(960 z^4)) (6350400 + 3024000 z + 1050840 z^2 + 292320 z^3 + 67500 z^4 + 13320 z^5 + 2325 z^6 + 392 z^7 + 96 z^8 + 128 z^9 - 16 z^10) + (1/(1920 z^(9/2))) ((Sqrt[Pi] (-6350400 - 7257600 z - 4195800 z^2 - 1638000 z^3 - 485100 z^4 - 115920 z^5 - 23205 z^6 - 3990 z^7 - 600 z^8 - 80 z^9 - 272 z^10 + 32 z^11) 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]