Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8768)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.8768.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(1/2), -(17/4)}, z] == (1/68918850) ((34459425 + 34459425 E^(4 Sqrt[z]) + 68918850 Sqrt[z] - 68918850 E^(4 Sqrt[z]) Sqrt[z] - 16216200 z - 16216200 E^(4 Sqrt[z]) z + 4324320 z^(3/2) - 4324320 E^(4 Sqrt[z]) z^(3/2) - 1330560 z^2 - 1330560 E^(4 Sqrt[z]) z^2 + 483840 z^(5/2) - 483840 E^(4 Sqrt[z]) z^(5/2) - 215040 z^3 - 215040 E^(4 Sqrt[z]) z^3 + 122880 z^(7/2) - 122880 E^(4 Sqrt[z]) z^(7/2) - 98304 z^4 - 98304 E^(4 Sqrt[z]) z^4 + 131072 z^(9/2) - 131072 E^(4 Sqrt[z]) z^(9/2) - 524288 z^5 - 524288 E^(4 Sqrt[z]) z^5 - 524288 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(21/4) Erf[Sqrt[2] z^(1/4)] + 524288 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(21/4) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 34459425 </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> <cn type='integer'> 34459425 </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]