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

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=-3/4, b_1`>=-11/2

For fixed z and a₁=-3/4, b_1`=-5/2

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

Input Form

HypergeometricPFQ[{-(3/4)}, {-(5/2), 21/4}, z] == (1/(171798691840 z^(17/4))) ((663 (-4 z^(1/4) (23916867975 + 31889157300 Sqrt[z] + 20060187840 z + 7309716480 z^(3/2) + 1507207680 z^2 + 157009920 z^(5/2) + 5160960 z^3 - 19267584 z^(7/2) + 458752 z^4 - 1835008 z^(9/2) + E^(4 Sqrt[z]) (23916867975 - 31889157300 Sqrt[z] + 20060187840 z - 7309716480 z^(3/2) + 1507207680 z^2 - 157009920 z^(5/2) + 5160960 z^3 + 19267584 z^(7/2) + 458752 z^4 + 1835008 z^(9/2))) + 7 E^(2 Sqrt[z]) Sqrt[2 Pi] (3416695425 - 778734000 z + 120384000 z^2 - 20275200 z^3 + 10813440 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + 7 E^(2 Sqrt[z]) Sqrt[2 Pi] (3416695425 - 778734000 z + 120384000 z^2 - 20275200 z^3 + 10813440 z^4 + 1048576 z^5) Erfi[Sqrt[2] z^(1/4)]))/ E^(2 Sqrt[z]))

Standard Form

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MathML Form

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</apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 778734000 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 3416695425 </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]