Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa2q)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.aa2q.01

Input Form

HypergeometricPFQ[{-(7/4)}, {9/2, 1/4}, z] == (1/(509184 z^(7/2))) ((184275 - 184275 E^(4 Sqrt[z]) + 368550 Sqrt[z] + 368550 E^(4 Sqrt[z]) Sqrt[z] + 249480 z - 249480 E^(4 Sqrt[z]) z + 7560 z^(3/2) + 7560 E^(4 Sqrt[z]) z^(3/2) - 40320 z^2 + 40320 E^(4 Sqrt[z]) z^2 + 40320 z^(5/2) + 40320 E^(4 Sqrt[z]) z^(5/2) - 43008 z^3 + 43008 E^(4 Sqrt[z]) z^3 + 67584 z^(7/2) + 67584 E^(4 Sqrt[z]) z^(7/2) - 294912 z^4 + 294912 E^(4 Sqrt[z]) z^4 - 8192 z^(9/2) - 8192 E^(4 Sqrt[z]) z^(9/2) + 32768 z^5 - 32768 E^(4 Sqrt[z]) z^5 + 2048 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(17/4) (-147 + 16 z) Erf[Sqrt[2] z^(1/4)] + 2048 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(17/4) (-147 + 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> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 184275 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 184275 </cn> </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]