Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8516)

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`=11/2

http://functions.wolfram.com/07.22.03.8516.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, 19/4}, z] == ((2 z (247213060959343854375 + 349692854021120610000 z + 270111901578725606400 z^2 + 670421062107655372800 z^3 - 219320091693151027200 z^4 + 18089431856169615360 z^5 - 556820543517491200 z^6 + 7190876912615424 z^7 - 38487201939456 z^8 + 68719476736 z^9) BesselI[-(1/4), Sqrt[z]]^2 - Sqrt[z] (599512933445504203125 + 636110418324350970000 z + 464979095933390438400 z^2 + 558251030904389222400 z^3 - 208871599605084979200 z^4 + 17753060436219002880 z^5 - 552390092484771840 z^6 + 7166937838649344 z^7 - 38444252266496 z^8 + 68719476736 z^9) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 (106594687074395520000 + 435978312420052276875 z + 481503373670274555600 z^2 + 377012663789553792000 z^3 + 621754200851786956800 z^4 - 215002699461594316800 z^5 + 17952966089606430720 z^6 - 555037731852386304 z^7 + 7181281955676160 z^8 - 38470022070272 z^9 + 68719476736 z^10) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(794617466300596224000 Sqrt[2] z^(15/4))

Standard Form

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MathML Form

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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]