Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7411)

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=5, b₁>=-23/4

For fixed z and a₁=5, b₁=-21/4

http://functions.wolfram.com/07.22.03.7411.01

Input Form

HypergeometricPFQ[{5}, {-(21/4), 21/4}, -z] == (1/(16515072 z^(17/4))) (-2 z^(1/4) (383016508875 - 162510648300 z + 32518886400 z^2 - 3519996480 z^3 + 270602496 z^4 - 20188160 z^5 + 770048 z^6) - Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((-383016508875 + 775337062500 z - 274378104000 z^2 + 41141580480 z^3 - 3649916160 z^4 + 275235840 z^5 - 17924096 z^6 + 262144 z^7) Cos[2 Sqrt[z]] - 2 Sqrt[z] (383016508875 - 264648384000 z + 57697239600 z^2 - 6429646080 z^3 + 496869120 z^4 - 37822464 z^5 + 1507328 z^6) Sin[2 Sqrt[z]]) - Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (383016508875 - 264648384000 z + 57697239600 z^2 - 6429646080 z^3 + 496869120 z^4 - 37822464 z^5 + 1507328 z^6) Cos[2 Sqrt[z]] + (-383016508875 + 775337062500 z - 274378104000 z^2 + 41141580480 z^3 - 3649916160 z^4 + 275235840 z^5 - 17924096 z^6 + 262144 z^7) Sin[2 Sqrt[z]]))

Standard Form

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MathML Form

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7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 17924096 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 275235840 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3649916160 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 41141580480 </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'> 274378104000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 775337062500 </cn> <ci> z </ci> </apply> <cn type='integer'> -383016508875 </cn> </apply> <apply> <sin /> 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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]