Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7799)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-11/4

http://functions.wolfram.com/07.22.03.7799.01

Input Form

HypergeometricPFQ[{6}, {-(11/4), 23/4}, -z] == -((1/(16777216 z^(19/4))) (19 (4 z^(3/4) (2341213875 - 772972200 z + 121413600 z^2 - 12337920 z^3 + 985088 z^4 + 65536 z^5) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-7023641625 + 4994589600 z - 1164240000 z^2 + 146119680 z^3 - 13708800 z^4 + 573440 z^5 + 131072 z^6) Cos[2 Sqrt[z]] - 7 (-1003377375 + 2051349300 z - 760914000 z^2 + 124848000 z^3 - 12936960 z^4 + 1105920 z^5 + 65536 z^6) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (7 (-1003377375 + 2051349300 z - 760914000 z^2 + 124848000 z^3 - 12936960 z^4 + 1105920 z^5 + 65536 z^6) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-7023641625 + 4994589600 z - 1164240000 z^2 + 146119680 z^3 - 13708800 z^4 + 573440 z^5 + 131072 z^6) Sin[2 Sqrt[z]]))))

Standard Form

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MathML Form

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<apply> <times /> <cn type='integer'> 4994589600 </cn> <ci> z </ci> </apply> <cn type='integer'> -7023641625 </cn> </apply> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </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]