Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7432)

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/07.22.03.7432.01

Input Form

HypergeometricPFQ[{5}, {-(19/4), 23/4}, z] == (1/(12582912 z^(19/4))) ((-16 E^(2 Sqrt[z]) z^(3/4) (756212081625 + 221367346200 z + 29156727600 z^2 + 2162160000 z^3 + 105752832 z^4 + 3471360 z^5 + 32768 z^6) - E^(4 Sqrt[z]) Sqrt[2 Pi] (2268636244875 - 4537272489750 Sqrt[z] + 4553192744100 z - 3056688835200 z^(3/2) + 1544690347200 z^2 - 627048021600 z^(5/2) + 213145732800 z^3 - 62477775360 z^(7/2) + 16155659520 z^4 - 3759275520 z^(9/2) + 800916480 z^5 - 156549120 z^(11/2) + 26836992 z^6 - 3538944 z^(13/2) + 262144 z^7) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (2268636244875 + 4537272489750 Sqrt[z] + 4553192744100 z + 3056688835200 z^(3/2) + 1544690347200 z^2 + 627048021600 z^(5/2) + 213145732800 z^3 + 62477775360 z^(7/2) + 16155659520 z^4 + 3759275520 z^(9/2) + 800916480 z^5 + 156549120 z^(11/2) + 26836992 z^6 + 3538944 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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4553192744100 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 4537272489750 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 2268636244875 </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]