Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8754)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.8754.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(3/2), 17/4}, z] == ((2 Sqrt[z] (-28584816685425 + 48142849154400 z + 55030849251840 z^2 - 32573386137600 z^3 - 13428735344640 z^4 - 87110927253504 z^5 + 15044834230272 z^6 - 529891590144 z^7 + 4294967296 z^8) BesselI[1/4, Sqrt[z]]^2 - 3 (-47641361142375 + 114116383180800 z - 57058191590400 z^2 - 106240085360640 z^3 - 70599414251520 z^4 - 74700973670400 z^5 + 14587520876544 z^6 - 526133493760 z^7 + 4294967296 z^8) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (142924083427125 - 37444438231200 z + 44831436249600 z^2 + 94150766223360 z^3 + 65446009896960 z^4 + 76335965798400 z^5 - 14651643396096 z^6 + 526670364672 z^7 - 4294967296 z^8) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(85608187822080 Sqrt[2] z^(11/4))

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]