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

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=15/4, b_1`>=-11/2

For fixed z and a₁=15/4, b_1`=-5/2

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

Input Form

HypergeometricPFQ[{15/4}, {-(5/2), 23/4}, z] == (1/(67108864 z^(19/4))) ((19 (-4 z^(1/4) (-524644745625 - 699526327500 Sqrt[z] - 540323784000 z - 294053760000 z^(3/2) - 121542220800 z^2 - 39920025600 z^(5/2) - 10674585600 z^3 - 2339635200 z^(7/2) - 412876800 z^4 - 54525952 z^(9/2) - 4194304 z^5 + E^(4 Sqrt[z]) (524644745625 - 699526327500 Sqrt[z] + 540323784000 z - 294053760000 z^(3/2) + 121542220800 z^2 - 39920025600 z^(5/2) + 10674585600 z^3 - 2339635200 z^(7/2) + 412876800 z^4 - 54525952 z^(9/2) + 4194304 z^5)) + 1206079875 E^(2 Sqrt[z]) Sqrt[2 Pi] (-435 + 16 z) Erf[Sqrt[2] z^(1/4)] - 1206079875 E^(2 Sqrt[z]) Sqrt[2 Pi] (-435 + 16 z) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<apply> <plus /> <apply> <times /> <cn type='integer'> 16 </cn> <ci> z </ci> </apply> <cn type='integer'> -435 </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> </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]