Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7742)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-17/4

http://functions.wolfram.com/07.22.03.7742.01

Input Form

HypergeometricPFQ[{6}, {-(17/4), 21/4}, z] == (1/(125829120 z^(17/4))) ((24 E^(2 Sqrt[z]) z^(1/4) (-20158763625 - 9340531200 z - 2108106000 z^2 - 290062080 z^3 - 38954240 z^4 - 4874240 z^5 + 65536 z^6) - E^(4 Sqrt[z]) Sqrt[2 Pi] (-60476290875 + 120952581750 Sqrt[z] - 124783659000 z + 88297209000 z^(3/2) - 48291843600 z^2 + 21859437600 z^(5/2) - 8602070400 z^3 + 3069792000 z^(7/2) - 1070150400 z^4 + 412853760 z^(9/2) - 169973760 z^5 + 56279040 z^(11/2) - 9830400 z^6 - 655360 z^(13/2) + 524288 z^7) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (60476290875 + 120952581750 Sqrt[z] + 124783659000 z + 88297209000 z^(3/2) + 48291843600 z^2 + 21859437600 z^(5/2) + 8602070400 z^3 + 3069792000 z^(7/2) + 1070150400 z^4 + 412853760 z^(9/2) + 169973760 z^5 + 56279040 z^(11/2) + 9830400 z^6 - 655360 z^(13/2) - 524288 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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</cn> </apply> </apply> <apply> <times /> <cn type='integer'> 88297209000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 124783659000 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 120952581750 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 60476290875 </cn> </apply> <apply> <ci> Erfi </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> </apply> </apply> </annotation-xml> </semantics> </math>

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]