Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9662)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9662.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, 13/4}, z] == (4 (44595048960000 + 89190097920000 Sqrt[z] - 5096577024000 z - 129113284608000 z^(3/2) + 463448737382400 z^2 - 221598716914575 z^(5/2) + 719320158225900 z^3 - 293472363492000 z^(7/2) + 1536159761136000 z^4 + 160746400362240 z^(9/2) - 685037173201920 z^5 - 15483504476160 z^(11/2) + 63305085419520 z^6 + 474140835840 z^(13/2) - 1911823269888 z^7 - 5144313856 z^(15/2) + 20627587072 z^8 + 16777216 z^(17/2) - 67108864 z^9 + E^(4 Sqrt[z]) (-44595048960000 + 89190097920000 Sqrt[z] + 5096577024000 z - 129113284608000 z^(3/2) - 463448737382400 z^2 - 221598716914575 z^(5/2) - 719320158225900 z^3 - 293472363492000 z^(7/2) - 1536159761136000 z^4 + 160746400362240 z^(9/2) + 685037173201920 z^5 - 15483504476160 z^(11/2) - 63305085419520 z^6 + 474140835840 z^(13/2) + 1911823269888 z^7 - 5144313856 z^(15/2) - 20627587072 z^8 + 16777216 z^(17/2) + 67108864 z^9)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (1352359272639375 + 2330219054394000 z + 6579442035936000 z^2 - 2784949009920000 z^3 + 254623909478400 z^4 - 7662663106560 z^5 + 82560679936 z^6 - 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (1352359272639375 + 2330219054394000 z + 6579442035936000 z^2 - 2784949009920000 z^3 + 254623909478400 z^4 - 7662663106560 z^5 + 82560679936 z^6 - 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (22975442268979200 z^(9/2))

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]