Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7410)

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=-21/4

http://functions.wolfram.com/07.22.03.7410.01

Input Form

HypergeometricPFQ[{5}, {-(21/4), 21/4}, z] == (1/(66060288 z^(17/4))) ((-8 E^(2 Sqrt[z]) z^(1/4) (383016508875 + 162510648300 z + 32518886400 z^2 + 3519996480 z^3 + 270602496 z^4 + 20188160 z^5 + 770048 z^6) + E^(4 Sqrt[z]) Sqrt[2 Pi] (383016508875 - 766033017750 Sqrt[z] + 775337062500 z - 529296768000 z^(3/2) + 274378104000 z^2 - 115394479200 z^(5/2) + 41141580480 z^3 - 12859292160 z^(7/2) + 3649916160 z^4 - 993738240 z^(9/2) + 275235840 z^5 - 75644928 z^(11/2) + 17924096 z^6 - 3014656 z^(13/2) + 262144 z^7) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (383016508875 + 766033017750 Sqrt[z] + 775337062500 z + 529296768000 z^(3/2) + 274378104000 z^2 + 115394479200 z^(5/2) + 41141580480 z^3 + 12859292160 z^(7/2) + 3649916160 z^4 + 993738240 z^(9/2) + 275235840 z^5 + 75644928 z^(11/2) + 17924096 z^6 + 3014656 z^(13/2) + 262144 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 383016508875 </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]