Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aes5)

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=5/2, b₁>=-11/2

For fixed z and a₁=1, a₂=5/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.aes5.01

Input Form

HypergeometricPFQ[{1, 5/2}, {-(9/2), -(9/2)}, -z] == (1/2679075) (2679075 - 330750 z + 94500 z^2 - 68040 z^3 + 166320 z^4 - 4324320 z^5 + 88441920 z^6 - 173550720 z^7 + 107729664 z^8 - 28442112 z^9 + 3515392 z^10 - 198656 z^11 + 4096 z^12) - (1/2679075) ((4096 Sqrt[Pi] (-5040 z^(11/2) + 35280 z^(13/2) - 52920 z^(15/2) + 29400 z^(17/2) - 7350 z^(19/2) + 882 z^(21/2) - 49 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]