Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8528)

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`=-11/2

http://functions.wolfram.com/07.22.03.8528.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(11/2), -(17/4)}, z] == (1/206756550) ((103378275 + 103378275 E^(4 Sqrt[z]) + 206756550 Sqrt[z] - 206756550 E^(4 Sqrt[z]) Sqrt[z] + 183537900 z + 183537900 E^(4 Sqrt[z]) z + 91400400 z^(3/2) - 91400400 E^(4 Sqrt[z]) z^(3/2) + 25855200 z^2 + 25855200 E^(4 Sqrt[z]) z^2 + 3356640 z^(5/2) - 3356640 E^(4 Sqrt[z]) z^(5/2) - 6720 z^3 - 6720 E^(4 Sqrt[z]) z^3 + 3840 z^(7/2) - 3840 E^(4 Sqrt[z]) z^(7/2) - 3072 z^4 - 3072 E^(4 Sqrt[z]) z^4 + 4096 z^(9/2) - 4096 E^(4 Sqrt[z]) z^(9/2) - 16384 z^5 - 16384 E^(4 Sqrt[z]) z^5 - 16384 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(21/4) Erf[Sqrt[2] z^(1/4)] + 16384 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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<sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 103378275 </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]