Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7763)

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/07.22.03.7763.01

Input Form

HypergeometricPFQ[{6}, {-(15/4), 23/4}, -z] == -((1/(125829120 z^(19/4))) (19 (4 z^(3/4) (39800635875 - 12932419500 z + 1978376400 z^2 - 190270080 z^3 + 14242560 z^4 + 73728 z^5 - 65536 z^6) - Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((119401907625 - 243486243000 z + 89221532400 z^2 - 14270256000 z^3 + 1399507200 z^4 - 109025280 z^5 + 524288 z^7) Cos[2 Sqrt[z]] - 30 Sqrt[z] (-7960127175 + 5618913300 z - 1286485200 z^2 + 155675520 z^3 - 13348608 z^4 + 745472 z^5 + 65536 z^6) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (30 Sqrt[z] (-7960127175 + 5618913300 z - 1286485200 z^2 + 155675520 z^3 - 13348608 z^4 + 745472 z^5 + 65536 z^6) Cos[2 Sqrt[z]] + (119401907625 - 243486243000 z + 89221532400 z^2 - 14270256000 z^3 + 1399507200 z^4 - 109025280 z^5 + 524288 z^7) Sin[2 Sqrt[z]]))))

Standard Form

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MathML Form

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</apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 14270256000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 89221532400 </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'> 243486243000 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 119401907625 </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]