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

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=1, a₂>=1

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

For fixed z and a₁=1, a₂=11/2, b₁=-9/2

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

Input Form

HypergeometricPFQ[{1, 11/2}, {-(9/2), -(3/2)}, -z] == (1/2679075) (2679075 - 2182950 z + 8108100 z^2 + 48648600 z^3 + 183783600 z^4 + 1396755360 z^5 - 3426010560 z^6 + 2304516480 z^7 - 676220160 z^8 + 99555840 z^9 - 7601152 z^10 + 284672 z^11 - 4096 z^12) + (1/2679075) ((4096 Sqrt[Pi] (-604800 z^(11/2) + 1058400 z^(13/2) - 635040 z^(15/2) + 176400 z^(17/2) - 25200 z^(19/2) + 1890 z^(21/2) - 70 z^(23/2) + z^(25/2)) 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]