Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7385)

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=-23/4

http://functions.wolfram.com/07.22.03.7385.01

Input Form

HypergeometricPFQ[{5}, {-(23/4), 15/4}, -z] == (1/(161095680 z^(11/4))) (4 z^(3/4) (-1206079875 + 527026500 z - 108409680 z^2 - 11852160 z^3 + 3083520 z^4 + 45056 z^5) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (5 (723647925 - 1556755200 z + 732972240 z^2 - 172972800 z^3 - 14466816 z^4 + 4792320 z^5 + 65536 z^6) Cos[2 Sqrt[z]] + 2 Sqrt[z] (3618239625 - 2959456500 z + 1005404400 z^2 - 86486400 z^3 - 34993920 z^4 + 1597440 z^5 + 65536 z^6) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (3618239625 - 2959456500 z + 1005404400 z^2 - 86486400 z^3 - 34993920 z^4 + 1597440 z^5 + 65536 z^6) Cos[2 Sqrt[z]] - 5 (723647925 - 1556755200 z + 732972240 z^2 - 172972800 z^3 - 14466816 z^4 + 4792320 z^5 + 65536 z^6) Sin[2 Sqrt[z]]))

Standard Form

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MathML Form

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</cn> <apply> <times /> <cn type='integer'> 1556755200 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 723647925 </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]