Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7095)

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=4, b₁>=-23/4

For fixed z and a₁=4, b₁=-23/4

http://functions.wolfram.com/07.22.03.7095.01

Input Form

HypergeometricPFQ[{4}, {-(23/4), 15/4}, -z] == (1/(10068480 z^(11/4))) (4 z^(3/4) (-241215975 + 89189100 z - 16099920 z^2 + 272256 z^3 + 180480 z^4 - 4096 z^5) - Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((-723647925 + 1508106600 z - 616215600 z^2 + 121080960 z^3 - 3144960 z^4 - 1357824 z^5 + 32768 z^6) Cos[2 Sqrt[z]] - 78 Sqrt[z] (18555075 - 13929300 z + 3825360 z^2 - 443520 z^3 - 32000 z^4 + 4096 z^5) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (78 Sqrt[z] (18555075 - 13929300 z + 3825360 z^2 - 443520 z^3 - 32000 z^4 + 4096 z^5) Cos[2 Sqrt[z]] + (-723647925 + 1508106600 z - 616215600 z^2 + 121080960 z^3 - 3144960 z^4 - 1357824 z^5 + 32768 z^6) Sin[2 Sqrt[z]]))

Standard Form

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MathML Form

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</cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 121080960 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 616215600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1508106600 </cn> <ci> z </ci> </apply> <cn type='integer'> -723647925 </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> </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]