Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7471)

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=-15/4

http://functions.wolfram.com/07.22.03.7471.01

Input Form

HypergeometricPFQ[{5}, {-(15/4), 19/4}, -z] == (1/(786432 z^(15/4))) (4 z^(3/4) (156080925 - 54054000 z + 9313920 z^2 - 1056768 z^3 - 31232 z^4 + 8192 z^5) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((-468242775 + 964863900 z - 371725200 z^2 + 66890880 z^3 - 8144640 z^4 - 172032 z^5 + 65536 z^6) Cos[2 Sqrt[z]] - 2 Sqrt[z] (468242775 - 340540200 z + 84157920 z^2 - 12337920 z^3 + 860160 z^4 + 131072 z^5) Sin[2 Sqrt[z]]) - Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (468242775 - 340540200 z + 84157920 z^2 - 12337920 z^3 + 860160 z^4 + 131072 z^5) Cos[2 Sqrt[z]] + (-468242775 + 964863900 z - 371725200 z^2 + 66890880 z^3 - 8144640 z^4 - 172032 z^5 + 65536 z^6) Sin[2 Sqrt[z]]))

Standard Form

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MathML Form

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</ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 66890880 </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'> 371725200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 964863900 </cn> <ci> z </ci> </apply> <cn type='integer'> -468242775 </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]