Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a94e)

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

For fixed z and a₁=-11/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.a94e.01

Input Form

HypergeometricPFQ[{-(11/4)}, {5/2, 13/4}, z] == (1/(4634705920 z^(9/4))) ((4 z^(1/4) (-11486475 + 60378780 Sqrt[z] - 44647680 z + 266999040 z^(3/2) + 40215040 z^2 - 171489280 z^(5/2) - 3768320 z^3 + 15269888 z^(7/2) + 65536 z^4 - 262144 z^(9/2) + E^(4 Sqrt[z]) (-11486475 - 60378780 Sqrt[z] - 44647680 z - 266999040 z^(3/2) + 40215040 z^2 + 171489280 z^(5/2) - 3768320 z^3 - 15269888 z^(7/2) + 65536 z^4 + 262144 z^(9/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (-11486475 - 183783600 z - 1176215040 z^2 + 697016320 z^3 - 61276160 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-11486475 - 183783600 z - 1176215040 z^2 + 697016320 z^3 - 61276160 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> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 183783600 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -11486475 </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]