Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa3k)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.aa3k.01

Input Form

HypergeometricPFQ[{-(7/4)}, {11/2, -(17/4)}, z] == (1/(937747200 Sqrt[2] z^(15/4))) ((4 z (-724524379425 - 59144847300 z - 1982232000 z^2 + 698286080 z^3 + 79953920 z^4 + 2097152 z^5) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-2173573138275 - 591448473000 z - 18236534400 z^2 + 375889920 z^3 + 40632320 z^4 + 1048576 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (6520719414825 + 3016387212300 z + 328158507600 z^2 - 3347769600 z^3 + 2876375040 z^4 + 321912832 z^5 + 8388608 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)

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]