Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7430)

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=5, b₁>=-23/4

For fixed z and a₁=5, b₁=-19/4

http://functions.wolfram.com/07.22.03.7430.01

Input Form

HypergeometricPFQ[{5}, {-(19/4), 19/4}, z] == (1/(29884416 z^(15/4))) ((48 E^(2 Sqrt[z]) z^(3/4) (-884458575 - 299999700 z - 49729680 z^2 - 5402752 z^3 - 65280 z^4 + 36864 z^5) - E^(4 Sqrt[z]) Sqrt[2 Pi] (7960127175 - 15920254350 Sqrt[z] + 16345929600 z - 11464853400 z^(3/2) + 6194588400 z^2 - 2763240480 z^(5/2) + 1072431360 z^3 - 380540160 z^(7/2) + 122653440 z^4 - 30051840 z^(9/2) + 2236416 z^5 + 1916928 z^(11/2) - 851968 z^6 + 131072 z^(13/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (7960127175 + 15920254350 Sqrt[z] + 16345929600 z + 11464853400 z^(3/2) + 6194588400 z^2 + 2763240480 z^(5/2) + 1072431360 z^3 + 380540160 z^(7/2) + 122653440 z^4 + 30051840 z^(9/2) + 2236416 z^5 - 1916928 z^(11/2) - 851968 z^6 - 131072 z^(13/2)) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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type='integer'> 2763240480 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6194588400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 11464853400 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16345929600 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 15920254350 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 7960127175 </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]