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

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=-5/4, b_1`>=-11/2

For fixed z and a₁=-5/4, b_1`=9/2

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

Input Form

HypergeometricPFQ[{-(5/4)}, {9/2, -(1/4)}, z] == (1/(160512 z^(7/2))) ((259875 - 259875 E^(4 Sqrt[z]) + 519750 Sqrt[z] + 519750 E^(4 Sqrt[z]) Sqrt[z] + 388080 z - 388080 E^(4 Sqrt[z]) z + 83160 z^(3/2) + 83160 E^(4 Sqrt[z]) z^(3/2) - 30240 z^2 + 30240 E^(4 Sqrt[z]) z^2 + 13440 z^(5/2) + 13440 E^(4 Sqrt[z]) z^(5/2) - 7680 z^3 + 7680 E^(4 Sqrt[z]) z^3 + 6144 z^(7/2) + 6144 E^(4 Sqrt[z]) z^(7/2) - 8192 z^4 + 8192 E^(4 Sqrt[z]) z^4 + 32768 z^(9/2) + 32768 E^(4 Sqrt[z]) z^(9/2) + 32768 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(19/4) Erf[Sqrt[2] z^(1/4)] - 32768 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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<power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 259875 </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]