Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8lo)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.a8lo.01

Input Form

HypergeometricPFQ[{-(13/4)}, {1/2, 11/4}, z] == (1/(692060160 z^(7/4))) ((-4 z^(1/4) (-2027025 - 2702700 Sqrt[z] + 8648640 z - 73328640 z^(3/2) - 20559360 z^2 + 90163200 z^(5/2) + 2867200 z^3 - 11665408 z^(7/2) - 65536 z^4 + 262144 z^(9/2) + E^(4 Sqrt[z]) (2027025 - 2702700 Sqrt[z] - 8648640 z - 73328640 z^(3/2) + 20559360 z^2 + 90163200 z^(5/2) - 2867200 z^3 - 11665408 z^(7/2) + 65536 z^4 + 262144 z^(9/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (2027025 - 10810800 z - 345945600 z^2 + 369008640 z^3 - 46858240 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (2027025 - 10810800 z - 345945600 z^2 + 369008640 z^3 - 46858240 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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<times /> <cn type='integer'> 345945600 </cn> <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'> 10810800 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 2027025 </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]