Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8281)

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`=1/2

http://functions.wolfram.com/07.22.03.8281.01

Input Form

HypergeometricPFQ[{-(23/4)}, {1/2, 23/4}, -z] == ((2 Sqrt[z] (-3632415580300381875 + 1758211238868084000 z + 557381651482656000 z^2 + 31087081215590400 z^3 + 10660404913127424000 z^4 + 39964470320981606400 z^5 + 13562189080669716480 z^6 + 1159150931615416320 z^7 + 33473158333857792 z^8 + 348682624958464 z^9 + 1099511627776 z^10) BesselJ[-(1/4), Sqrt[z]]^2 - (-10897246740901145625 + 21879962083691712000 z + 5366164527019296000 z^2 + 2207182766306918400 z^3 - 870438274036531200 z^4 + 33096365963948851200 z^5 + 12890059494276464640 z^6 + 1138803094553886720 z^7 + 33257078529196032 z^8 + 347995430191104 z^9 + 1099511627776 z^10) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (10897246740901145625 + 1367497630230732000 z + 1093633802451590400 z^2 + 1336744492270387200 z^3 + 4352191370182656000 z^4 + 36971236009967616000 z^5 + 13284855434906173440 z^6 + 1150916822178988032 z^7 + 33386417174347776 z^8 + 348407747051520 z^9 + 1099511627776 z^10) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(23416287339007180800 Sqrt[2] z^(17/4))

Standard Form

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MathML Form

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<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]