Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8074)

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`=-7/2

http://functions.wolfram.com/07.22.03.8074.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(7/2), 9/4}, z] == (-4 z^(1/4) (-498438430875 - 664584574500 Sqrt[z] + 186870045600 z - 825510268800 z^(3/2) + 73124755200 z^2 - 280357862400 z^(5/2) + 14352629760 z^3 - 57424281600 z^(7/2) + 2277703680 z^4 - 11422924800 z^(9/2) - 828375040 z^5 + 3363831808 z^(11/2) + 16777216 z^6 - 67108864 z^(13/2) + E^(4 Sqrt[z]) (-498438430875 + 664584574500 Sqrt[z] + 186870045600 z + 825510268800 z^(3/2) + 73124755200 z^2 + 280357862400 z^(5/2) + 14352629760 z^3 + 57424281600 z^(7/2) + 2277703680 z^4 + 11422924800 z^(9/2) - 828375040 z^5 - 3363831808 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-498438430875 + 2938163382000 z + 3134040940800 z^2 + 1085382144000 z^3 + 225533952000 z^4 + 48113909760 z^5 - 13505658880 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-498438430875 + 2938163382000 z + 3134040940800 z^2 + 1085382144000 z^3 + 225533952000 z^4 + 48113909760 z^5 - 13505658880 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(17757005414400 z^(5/4))

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]