Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8ce)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8ce.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, 13/4}, z] == (-4 (-83825280000 - 167650560000 Sqrt[z] - 9580032000 z + 204374016000 z^(3/2) - 656551526400 z^2 + 278486571825 z^(5/2) - 868553601300 z^3 + 315119019600 z^(7/2) - 1579225032000 z^4 - 133071459840 z^(9/2) + 558963947520 z^5 + 9523077120 z^(11/2) - 38662471680 z^6 - 193658880 z^(13/2) + 777781248 z^7 + 1048576 z^(15/2) - 4194304 z^8 + E^(4 Sqrt[z]) (83825280000 - 167650560000 Sqrt[z] + 9580032000 z + 204374016000 z^(3/2) + 656551526400 z^2 + 278486571825 z^(5/2) + 868553601300 z^3 + 315119019600 z^(7/2) + 1579225032000 z^4 - 133071459840 z^(9/2) - 558963947520 z^5 + 9523077120 z^(11/2) + 38662471680 z^6 - 193658880 z^(13/2) - 777781248 z^7 + 1048576 z^(15/2) + 4194304 z^8)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (1923697400625 + 2841153084000 z + 6685066080000 z^2 - 2263726080000 z^3 + 155226931200 z^4 - 3114270720 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (1923697400625 + 2841153084000 z + 6685066080000 z^2 - 2263726080000 z^3 + 155226931200 z^4 - 3114270720 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(22177067827200 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]