Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7121)

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=4, b₁>=-23/4

For fixed z and a₁=4, b₁=-21/4

http://functions.wolfram.com/07.22.03.7121.01

Input Form

HypergeometricPFQ[{4}, {-(21/4), 21/4}, -z] == (1/(1032192 z^(17/4))) (2 z^(1/4) (383016508875 - 150105255300 z + 27070243200 z^2 - 2361078720 z^3 + 114741504 z^4 - 2868224 z^5 + 16384 z^6) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (383016508875 - 252242991000 z + 48940491600 z^2 - 4405864320 z^3 + 218592000 z^4 - 5584896 z^5 + 32768 z^6) Cos[2 Sqrt[z]] + (-383016508875 + 762931669500 z - 249080832000 z^2 + 31852941120 z^3 - 2106466560 z^4 + 77552640 z^5 - 1163264 z^6) Sin[2 Sqrt[z]]) - Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((383016508875 - 762931669500 z + 249080832000 z^2 - 31852941120 z^3 + 2106466560 z^4 - 77552640 z^5 + 1163264 z^6) Cos[2 Sqrt[z]] + 2 Sqrt[z] (383016508875 - 252242991000 z + 48940491600 z^2 - 4405864320 z^3 + 218592000 z^4 - 5584896 z^5 + 32768 z^6) Sin[2 Sqrt[z]]))

Standard Form

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MathML Form

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<cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 48940491600 </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'> 252242991000 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 383016508875 </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]