Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6831)

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/07.22.03.6831.01

Input Form

HypergeometricPFQ[{3}, {-(21/4), 21/4}, -z] == (1/(86016 z^(17/4))) (2 z^(1/4) (-76603301775 + 27539972460 z - 4454049600 z^2 + 302702400 z^3 - 9224448 z^4 + 93184 z^5) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((76603301775 - 150105255300 z + 44886441600 z^2 - 4782697920 z^3 + 225434880 z^4 - 4359168 z^5 + 16384 z^6) Cos[2 Sqrt[z]] - 90 Sqrt[z] (-1702295595 + 1065944880 z - 181477296 z^2 + 12739584 z^3 - 397056 z^4 + 4096 z^5) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (90 Sqrt[z] (-1702295595 + 1065944880 z - 181477296 z^2 + 12739584 z^3 - 397056 z^4 + 4096 z^5) Cos[2 Sqrt[z]] + (76603301775 - 150105255300 z + 44886441600 z^2 - 4782697920 z^3 + 225434880 z^4 - 4359168 z^5 + 16384 z^6) Sin[2 Sqrt[z]]))

Standard Form

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MathML Form

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/> <cn type='integer'> 4782697920 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 44886441600 </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'> 150105255300 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 76603301775 </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]