Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7676)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-23/4

http://functions.wolfram.com/07.22.03.7676.01

Input Form

HypergeometricPFQ[{6}, {-(23/4), 19/4}, z] == (1/(6873415680 z^(15/4))) ((-48 E^(2 Sqrt[z]) z^(3/4) (84023564625 + 31243212000 z + 5913507600 z^2 + 758309120 z^3 - 15983360 z^4 - 10403840 z^5 + 65536 z^6) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-756212081625 + 1512424163250 Sqrt[z] - 1577552476500 z + 1138539402000 z^(3/2) - 641512872000 z^2 + 302724021600 z^(5/2) - 126659332800 z^3 + 49643193600 z^(7/2) - 17470252800 z^4 + 4112908800 z^(9/2) + 177515520 z^5 - 614215680 z^(11/2) + 240680960 z^6 - 38010880 z^(13/2) - 1310720 z^7 + 1048576 z^(15/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (756212081625 + 1512424163250 Sqrt[z] + 1577552476500 z + 1138539402000 z^(3/2) + 641512872000 z^2 + 302724021600 z^(5/2) + 126659332800 z^3 + 49643193600 z^(7/2) + 17470252800 z^4 + 4112908800 z^(9/2) - 177515520 z^5 - 614215680 z^(11/2) - 240680960 z^6 - 38010880 z^(13/2) + 1310720 z^7 + 1048576 z^(15/2)) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]