Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8896)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.8896.01

Input Form

HypergeometricPFQ[{-(21/4)}, {3/2, 15/4}, z] == (-4 z^(1/4) (-33204585038625 - 44272780051500 Sqrt[z] + 86015686957200 z + 141672896164800 z^(3/2) + 993206619175680 z^2 - 5541087937674240 z^(5/2) - 773770378752000 z^3 + 3377273807093760 z^(7/2) + 107584608337920 z^4 - 443261609312256 z^(9/2) - 4520659648512 z^5 + 18273596866560 z^(11/2) + 64575504384 z^6 - 259107323904 z^(13/2) - 268435456 z^7 + 1073741824 z^(15/2) + E^(4 Sqrt[z]) (33204585038625 - 44272780051500 Sqrt[z] - 86015686957200 z + 141672896164800 z^(3/2) - 993206619175680 z^2 - 5541087937674240 z^(5/2) + 773770378752000 z^3 + 3377273807093760 z^(7/2) - 107584608337920 z^4 - 443261609312256 z^(9/2) + 4520659648512 z^5 + 18273596866560 z^(11/2) - 64575504384 z^6 - 259107323904 z^(13/2) + 268435456 z^7 + 1073741824 z^(15/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (33204585038625 - 121433910998400 z + 2266766338636800 z^2 - 24178840945459200 z^3 + 13816480540262400 z^4 - 1786373241569280 z^5 + 73287107346432 z^6 - 1037234601984 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (33204585038625 - 121433910998400 z + 2266766338636800 z^2 - 24178840945459200 z^3 + 13816480540262400 z^4 - 1786373241569280 z^5 + 73287107346432 z^6 - 1037234601984 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(70946846775705600 z^(11/4))

Standard Form

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MathML Form

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type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 18273596866560 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4520659648512 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 443261609312256 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 107584608337920 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3377273807093760 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 773770378752000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> 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<ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 13816480540262400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 24178840945459200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2266766338636800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 121433910998400 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 33204585038625 </cn> </apply> <apply> <ci> Erf </ci> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> 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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]