Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8576)

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`=-9/2

http://functions.wolfram.com/07.22.03.8576.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(9/2), -(17/4)}, z] == (1/18796050) ((9398025 + 9398025 E^(4 Sqrt[z]) + 18796050 Sqrt[z] - 18796050 E^(4 Sqrt[z]) Sqrt[z] + 16216200 z + 16216200 E^(4 Sqrt[z]) z + 7371000 z^(3/2) - 7371000 E^(4 Sqrt[z]) z^(3/2) + 1587600 z^2 + 1587600 E^(4 Sqrt[z]) z^2 + 30240 z^(5/2) - 30240 E^(4 Sqrt[z]) z^(5/2) - 13440 z^3 - 13440 E^(4 Sqrt[z]) z^3 + 7680 z^(7/2) - 7680 E^(4 Sqrt[z]) z^(7/2) - 6144 z^4 - 6144 E^(4 Sqrt[z]) z^4 + 8192 z^(9/2) - 8192 E^(4 Sqrt[z]) z^(9/2) - 32768 z^5 - 32768 E^(4 Sqrt[z]) z^5 - 32768 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(21/4) Erf[Sqrt[2] z^(1/4)] + 32768 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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</apply> </apply> </apply> </apply> <cn type='integer'> 9398025 </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]