Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6829)

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=3, b₁>=-23/4

For fixed z and a₁=3, b₁=-21/4

http://functions.wolfram.com/07.22.03.6829.01

Input Form

HypergeometricPFQ[{3}, {-(21/4), 17/4}, -z] == (1/(182784 z^(13/4))) (2 z^(1/4) (-1550674125 + 599999400 z - 105945840 z^2 + 8577408 z^3 - 300288 z^4 + 2048 z^5) - Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (33 (-46990125 + 93366000 z - 30073680 z^2 + 3709440 z^3 - 211200 z^4 + 4096 z^5) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-1550674125 + 1013512500 z - 192432240 z^2 + 16156800 z^3 - 582912 z^4 + 4096 z^5) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-1550674125 + 1013512500 z - 192432240 z^2 + 16156800 z^3 - 582912 z^4 + 4096 z^5) Cos[2 Sqrt[z]] - 33 (-46990125 + 93366000 z - 30073680 z^2 + 3709440 z^3 - 211200 z^4 + 4096 z^5) Sin[2 Sqrt[z]]))

Standard Form

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MathML Form

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</cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </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]