Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7xu)

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.a7xu.01

Input Form

HypergeometricPFQ[{-(15/4)}, {-(11/2), 17/4}, z] == (13 (-4 z^(1/4) (-329362868401875 - 439150491202500 Sqrt[z] - 234213595308000 z - 44612113392000 z^(3/2) - 575640172800 z^2 - 9419566464000 z^(5/2) + 559246786560 z^3 - 2106641940480 z^(7/2) + 38665912320 z^4 - 150810132480 z^(9/2) + 1226833920 z^5 - 4857004032 z^(11/2) + 16777216 z^6 - 67108864 z^(13/2) + E^(4 Sqrt[z]) (-329362868401875 + 439150491202500 Sqrt[z] - 234213595308000 z + 44612113392000 z^(3/2) - 575640172800 z^2 + 9419566464000 z^(5/2) + 559246786560 z^3 + 2106641940480 z^(7/2) + 38665912320 z^4 + 150810132480 z^(9/2) + 1226833920 z^5 + 4857004032 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-329362868401875 + 117106797654000 z - 36265330886400 z^2 + 35817610752000 z^3 + 8305532928000 z^4 + 599497113600 z^5 + 19377684480 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-329362868401875 + 117106797654000 z - 36265330886400 z^2 + 35817610752000 z^3 + 8305532928000 z^4 + 599497113600 z^5 + 19377684480 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/ (1904903895121920 z^(13/4))

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]