Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anv1)

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=11/2, a₂>=11/2

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

For fixed z and a₁=11/2, a₂=6, b₁=-1/2

http://functions.wolfram.com/07.25.03.anv1.01

Input Form

HypergeometricPFQ[{11/2, 6}, {-(1/2), 1/2}, -z] == (1/28350) (28350 + 3742200 z - 81081000 z^2 + 275675400 z^3 - 330810480 z^4 + 184633020 z^5 - 54646410 z^6 + 9150345 z^7 - 885900 z^8 + 48632 z^9 - 1392 z^10 + 16 z^11) + (1/56700) ((Sqrt[Pi] (-32432400 z^(3/2) + 308107800 z^(5/2) - 778377600 z^(7/2) + 808107300 z^(9/2) - 416584350 z^(11/2) + 117666675 z^(13/2) - 19141290 z^(15/2) + 1819080 z^(17/2) - 98640 z^(19/2) + 2800 z^(21/2) - 32 z^(23/2)) 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]