Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8425)

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`=7/2

http://functions.wolfram.com/07.22.03.8425.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, 23/4}, -z] == ((2 Sqrt[z] (43693083337700671875 + 47937554290505880000 z + 575250651486070560000 z^2 - 915573261841433395200 z^3 + 3695333765796642816000 z^4 + 1581137250479190835200 z^5 + 161954029379864494080 z^6 + 5962905916129935360 z^7 + 89670529069350912 z^8 + 547831668539392 z^9 + 1099511627776 z^10) BesselJ[-(1/4), Sqrt[z]]^2 - (131079250013102015625 - 55927146672256860000 z + 1365493970699258400000 z^2 - 1774647480633598771200 z^3 + 2922027276142382284800 z^4 + 1488970378717220044800 z^5 + 158371630188582666240 z^6 + 5907769230517862400 z^7 + 89329981112451072 z^8 + 547144473772032 z^9 + 1099511627776 z^10) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (-131079250013102015625 - 223708586689027440000 z + 1025395473372971500800 z^2 - 1433759301697779302400 z^3 + 3353837055921812275200 z^4 + 1542822786091922227200 z^5 + 160497342488311234560 z^6 + 5940700256604782592 z^7 + 89534000648945664 z^8 + 547556790632448 z^9 + 1099511627776 z^10) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(4668622288214556672000 Sqrt[2] z^(17/4))

Standard Form

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MathML Form

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</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'> 4668622288214556672000 </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]