Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7695)

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=-21/4

http://functions.wolfram.com/07.22.03.7695.01

Input Form

HypergeometricPFQ[{6}, {-(21/4), 9/4}, -z] == (1/(1283143680 z^(5/4))) (2 z^(1/4) (468242775 - 914434920 z - 45902880 z^2 + 87010560 z^3 + 8970240 z^4 + 557056 z^5) - Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((468242775 - 2305195200 z + 2095632000 z^2 + 681246720 z^3 - 21081600 z^4 - 6242304 z^5 + 131072 z^6) Cos[2 Sqrt[z]] + 6 Sqrt[z] (156080925 - 560290500 z + 6985440 z^2 + 58322880 z^3 + 5785600 z^4 + 376832 z^5) Sin[2 Sqrt[z]]) - Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (-6 Sqrt[z] (156080925 - 560290500 z + 6985440 z^2 + 58322880 z^3 + 5785600 z^4 + 376832 z^5) Cos[2 Sqrt[z]] + (468242775 - 2305195200 z + 2095632000 z^2 + 681246720 z^3 - 21081600 z^4 - 6242304 z^5 + 131072 z^6) Sin[2 Sqrt[z]]))

Standard Form

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MathML Form

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z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6985440 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 560290500 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 156080925 </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]