Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8473)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.8473.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, 23/4}, -z] == ((2 Sqrt[z] (-323328816698984971875 - 3251764099372648860000 z + 5121046534651695648000 z^2 - 4096693557911988633600 z^3 + 10382669033038744780800 z^4 + 3431616154536561868800 z^5 + 285093825407814205440 z^6 + 8822281660457287680 z^7 + 114394053042241536 z^8 + 614214683066368 z^9 + 1099511627776 z^10) BesselJ[-(1/4), Sqrt[z]]^2 - (-969986450096954915625 - 8277217707494015280000 z + 9442005102925563168000 z^2 - 7090724890986850713600 z^3 + 8630017128066642739200 z^4 + 3267012513928052736000 z^5 + 279765071916926238720 z^6 + 8751804275081871360 z^7 + 114012015701262336 z^8 + 613527488299008 z^9 + 1099511627776 z^10) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (969986450096954915625 - 6026421800259632772000 z + 7124406852968595590400 z^2 - 5744796158978872934400 z^3 + 9621829495086700953600 z^4 + 3363589410717066854400 z^5 + 282931830007529472000 z^6 + 8793921050803961856 z^7 + 114240928868204544 z^8 + 613939805159424 z^9 + 1099511627776 z^10) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(12338501761709899776000 Sqrt[2] z^(17/4))

Standard Form

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MathML Form

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type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 12338501761709899776000 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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]