Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7vy)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a7vy.01

Input Form

HypergeometricPFQ[{-(17/4)}, {11/2, -(3/4)}, z] == ((4 z (-130848702075 + 33231416400 z + 22185273600 z^2 - 26178969600 z^3 - 93413376000 z^4 + 30482694144 z^5 - 1570766848 z^6 + 16777216 z^7) BesselI[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-218081170125 + 36000701100 z - 13767062400 z^2 - 35996083200 z^3 - 34475212800 z^4 + 14566522880 z^5 - 778043392 z^6 + 8388608 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (-3271217551875 + 249235623000 z - 148563979200 z^2 + 115482931200 z^3 + 282252902400 z^4 + 288188006400 z^5 - 117284536320 z^6 + 6232735744 z^7 - 67108864 z^8) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(67594111200 Sqrt[2] z^(13/4))

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]