Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9l8)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.a9l8.01

Input Form

HypergeometricPFQ[{-(9/4)}, {7/2, -(5/4)}, z] == (1/(1404480 z^(5/2))) ((-467775 + 467775 E^(4 Sqrt[z]) - 935550 Sqrt[z] - 935550 E^(4 Sqrt[z]) Sqrt[z] - 540540 z + 540540 E^(4 Sqrt[z]) z + 166320 z^(3/2) + 166320 E^(4 Sqrt[z]) z^(3/2) - 60480 z^2 + 60480 E^(4 Sqrt[z]) z^2 + 26880 z^(5/2) + 26880 E^(4 Sqrt[z]) z^(5/2) - 15360 z^3 + 15360 E^(4 Sqrt[z]) z^3 + 12288 z^(7/2) + 12288 E^(4 Sqrt[z]) z^(7/2) - 16384 z^4 + 16384 E^(4 Sqrt[z]) z^4 + 65536 z^(9/2) + 65536 E^(4 Sqrt[z]) z^(9/2) + 65536 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(19/4) Erf[Sqrt[2] z^(1/4)] - 65536 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(19/4) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<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'> -467775 </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]