Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7409)

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/07.22.03.7409.01

Input Form

HypergeometricPFQ[{5}, {-(21/4), 17/4}, -z] == (1/(35094528 z^(13/4))) (-2 z^(1/4) (-4652022375 + 2286484200 z - 577296720 z^2 + 118790784 z^3 - 18589440 z^4 + 165888 z^5 + 32768 z^6) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (3 (-1550674125 + 3243240000 z - 1338377040 z^2 + 290062080 z^3 - 63740160 z^4 + 5316608 z^5 + 196608 z^6) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-4652022375 + 3527023500 z - 966485520 z^2 + 205476480 z^3 - 35202816 z^4 + 417792 z^5 + 65536 z^6) Sin[2 Sqrt[z]]) - Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-4652022375 + 3527023500 z - 966485520 z^2 + 205476480 z^3 - 35202816 z^4 + 417792 z^5 + 65536 z^6) Cos[2 Sqrt[z]] - 3 (-1550674125 + 3243240000 z - 1338377040 z^2 + 290062080 z^3 - 63740160 z^4 + 5316608 z^5 + 196608 z^6) Sin[2 Sqrt[z]]))

Standard Form

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MathML Form

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<apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3243240000 </cn> <ci> z </ci> </apply> <cn type='integer'> -1550674125 </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> </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]