Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6807)

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=-23/4

http://functions.wolfram.com/07.22.03.6807.01

Input Form

HypergeometricPFQ[{3}, {-(23/4), 19/4}, -z] == (1/(447488 z^(15/4))) (4 z^(3/4) (-16804712925 + 4318914600 z - 469188720 z^2 + 23788928 z^3 - 505088 z^4 + 2048 z^5) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((50414138775 - 99380981700 z + 30702672000 z^2 - 3491167680 z^3 + 181843200 z^4 - 3949568 z^5 + 16384 z^6) Cos[2 Sqrt[z]] + 2 Sqrt[z] (50414138775 - 32162130000 z + 5744859120 z^2 - 438197760 z^3 + 15276800 z^4 - 176128 z^5) Sin[2 Sqrt[z]]) - Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-50414138775 + 32162130000 z - 5744859120 z^2 + 438197760 z^3 - 15276800 z^4 + 176128 z^5) Cos[2 Sqrt[z]] + (50414138775 - 99380981700 z + 30702672000 z^2 - 3491167680 z^3 + 181843200 z^4 - 3949568 z^5 + 16384 z^6) Sin[2 Sqrt[z]]))

Standard Form

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MathML Form

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</apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3491167680 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 30702672000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 99380981700 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 50414138775 </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> </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]