Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8358)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8358.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, 5/4}, z] == (-4 (139549132800 + 279098265600 Sqrt[z] - 7814751436800 z - 7358849846775 z^(3/2) + 38070348453900 z^2 + 4063733286480 z^(5/2) - 17562245279040 z^3 - 493659809280 z^(7/2) + 2029721794560 z^4 + 19223715840 z^(9/2) - 77667926016 z^5 - 261292032 z^(11/2) + 1048313856 z^6 + 1048576 z^(13/2) - 4194304 z^7 + E^(4 Sqrt[z]) (-139549132800 + 279098265600 Sqrt[z] + 7814751436800 z - 7358849846775 z^(3/2) - 38070348453900 z^2 + 4063733286480 z^(5/2) + 17562245279040 z^3 - 493659809280 z^(7/2) - 2029721794560 z^4 + 19223715840 z^(9/2) + 77667926016 z^5 - 261292032 z^(11/2) - 1048313856 z^6 + 1048576 z^(13/2) + 4194304 z^7)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (45853950767625 - 163036269396000 z + 71664294240000 z^2 - 8175605760000 z^3 + 311451648000 z^4 - 4196401152 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (45853950767625 - 163036269396000 z + 71664294240000 z^2 - 8175605760000 z^3 + 311451648000 z^4 - 4196401152 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (297689333760000 z^(3/2))

Standard Form

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MathML 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]