Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8448)

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/07.22.03.8448.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, -(1/4)}, z] == ((-4 z (-8263584511875 + 5792379238800 z - 32721796800000 z^2 - 168867862732800 z^3 + 164545419064320 z^4 - 25125033738240 z^5 + 1104004251648 z^6 - 16072572928 z^7 + 67108864 z^8) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-24790753535625 + 12655089423900 z - 14744238062400 z^2 - 48832297113600 z^3 + 75260076756480 z^4 - 12230623641600 z^5 + 547035807744 z^6 - 8015314944 z^7 + 33554432 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (74372260606875 - 23799123394200 z + 36265330886400 z^2 - 164109780172800 z^3 - 543164822323200 z^4 + 634668306370560 z^5 - 99420749955072 z^6 + 4400049291264 z^7 - 64223182848 z^8 + 268435456 z^9) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (106487893512000 Sqrt[2] z^(11/4))

Standard Form

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MathML Form

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<ci> z </ci> <cn type='rational'> 11 <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]