Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a94m)

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

For fixed z and a₁=-11/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.a94m.01

Input Form

HypergeometricPFQ[{-(11/4)}, {5/2, 21/4}, z] == (4 z^(1/4) (-28222269075 - 37629692100 Sqrt[z] + 4631346720 z + 29111322240 z^(3/2) - 32345913600 z^2 + 105171010560 z^(5/2) - 48425287680 z^3 + 247988944896 z^(7/2) + 22194880512 z^4 - 92677079040 z^(9/2) - 1356857344 z^5 + 5477761024 z^(11/2) + 16777216 z^6 - 67108864 z^(13/2) + E^(4 Sqrt[z]) (-28222269075 + 37629692100 Sqrt[z] + 4631346720 z - 29111322240 z^(3/2) - 32345913600 z^2 - 105171010560 z^(5/2) - 48425287680 z^3 - 247988944896 z^(7/2) + 22194880512 z^4 + 92677079040 z^(9/2) - 1356857344 z^5 - 5477761024 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (-28222269075 + 34735100400 z - 61751289600 z^2 - 329340211200 z^3 - 1053888675840 z^4 + 374715973632 z^5 - 21961375744 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-28222269075 + 34735100400 z - 61751289600 z^2 - 329340211200 z^3 - 1053888675840 z^4 + 374715973632 z^5 - 21961375744 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(3607772528640 z^(17/4))

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]