Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7761)

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=-15/4

http://functions.wolfram.com/07.22.03.7761.01

Input Form

HypergeometricPFQ[{6}, {-(15/4), 19/4}, -z] == (1/(15728640 z^(15/4))) (12 z^(3/4) (260134875 - 102702600 z + 21621600 z^2 - 2932480 z^3 - 536576 z^4 + 32768 z^5) - Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (2341213875 - 1816214400 z + 518918400 z^2 - 100638720 z^3 + 3494400 z^4 + 3194880 z^5 + 131072 z^6) Cos[2 Sqrt[z]] + 13 (-180093375 + 379833300 z - 162162000 z^2 + 35683200 z^3 - 5564160 z^4 - 860160 z^5 + 65536 z^6) Sin[2 Sqrt[z]]) - Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (-13 (-180093375 + 379833300 z - 162162000 z^2 + 35683200 z^3 - 5564160 z^4 - 860160 z^5 + 65536 z^6) Cos[2 Sqrt[z]] + 2 Sqrt[z] (2341213875 - 1816214400 z + 518918400 z^2 - 100638720 z^3 + 3494400 z^4 + 3194880 z^5 + 131072 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'> 379833300 </cn> <ci> z </ci> </apply> <cn type='integer'> -180093375 </cn> </apply> <apply> <cos /> <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]