Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8302)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.8302.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, -(3/4)}, z] == (1/(1503684000 Sqrt[z])) ((4 (-45426150 + 97108200 Sqrt[z] - 169192800 z + 367516800 z^(3/2) - 1946649600 z^2 - 215403615 z^(5/2) + 920459820 z^3 + 21487920 z^(7/2) - 87664320 z^4 - 584960 z^(9/2) + 2352128 z^5 + 4096 z^(11/2) - 16384 z^6 + E^(4 Sqrt[z]) (45426150 + 97108200 Sqrt[z] + 169192800 z + 367516800 z^(3/2) + 1946649600 z^2 - 215403615 z^(5/2) - 920459820 z^3 + 21487920 z^(7/2) + 87664320 z^4 - 584960 z^(9/2) - 2352128 z^5 + 4096 z^(11/2) + 16384 z^6)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (-8365982625 + 3744216000 z - 352396800 z^2 + 9420800 z^3 - 65536 z^4) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (-8365982625 + 3744216000 z - 352396800 z^2 + 9420800 z^3 - 65536 z^4) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<apply> <times /> <cn type='integer'> 1946649600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 367516800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 169192800 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 97108200 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 45426150 </cn> </apply> </apply> <cn type='integer'> -45426150 </cn> </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]