Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7698)

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=-21/4

http://functions.wolfram.com/07.22.03.7698.01

Input Form

HypergeometricPFQ[{6}, {-(21/4), 17/4}, z] == (1/(2807562240 z^(13/4))) ((8 E^(2 Sqrt[z]) z^(1/4) (-32564156625 - 17708090400 z - 5221616400 z^2 - 1505629440 z^3 - 254926080 z^4 + 11304960 z^5 + 458752 z^6) + E^(4 Sqrt[z]) Sqrt[2 Pi] (32564156625 - 65128313250 Sqrt[z] + 69810741000 z - 52783731000 z^(3/2) + 32010778800 z^2 - 16799983200 z^(5/2) + 8801654400 z^3 - 5149267200 z^(7/2) + 2754259200 z^4 - 995258880 z^(9/2) + 149022720 z^5 + 39567360 z^(11/2) - 21626880 z^6 + 1966080 z^(13/2) + 524288 z^7) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (32564156625 + 65128313250 Sqrt[z] + 69810741000 z + 52783731000 z^(3/2) + 32010778800 z^2 + 16799983200 z^(5/2) + 8801654400 z^3 + 5149267200 z^(7/2) + 2754259200 z^4 + 995258880 z^(9/2) + 149022720 z^5 - 39567360 z^(11/2) - 21626880 z^6 - 1966080 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 type='integer'> 52783731000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 69810741000 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 65128313250 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 32564156625 </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]