Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9dw)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.a9dw.01

Input Form

HypergeometricPFQ[{-(9/4)}, {-(5/2), 19/4}, z] == (77 (4 z^(1/4) (54273594375 + 72364792500 Sqrt[z] + 38945415600 z + 7819156800 z^(3/2) - 351336960 z^2 + 672122880 z^(5/2) - 144875520 z^3 + 512655360 z^(7/2) - 18677760 z^4 + 71565312 z^(9/2) - 1048576 z^5 + 4194304 z^(11/2) + E^(4 Sqrt[z]) (-54273594375 + 72364792500 Sqrt[z] - 38945415600 z + 7819156800 z^(3/2) + 351336960 z^2 + 672122880 z^(5/2) + 144875520 z^3 + 512655360 z^(7/2) + 18677760 z^4 + 71565312 z^(9/2) + 1048576 z^5 + 4194304 z^(11/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-54273594375 + 18946418400 z - 5155488000 z^2 + 2156544000 z^3 + 1990656000 z^4 + 283115520 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-54273594375 + 18946418400 z - 5155488000 z^2 + 2156544000 z^3 + 1990656000 z^4 + 283115520 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)]))/ E^(2 Sqrt[z])/(1030792151040 z^(15/4))

Standard Form

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MathML Form

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type='integer'> 18946418400 </cn> <ci> z </ci> </apply> <cn type='integer'> -54273594375 </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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 16777216 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 283115520 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> 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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]