Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1675)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-5/2, b_1`>=-11/2

For fixed z and a₁=-5/2, b₁=5

http://functions.wolfram.com/07.22.03.1675.01

Input Form

HypergeometricPFQ[{-(5/2)}, {5, 6}, z] == -((1/(6087156075 z^4)) (512 (2 z (-79053975 - 59816475 z - 22998600 z^2 - 15015600 z^3 + 3392640 z^4 - 125184 z^5 + 1024 z^6) BesselI[0, Sqrt[z]]^2 - 4 Sqrt[z] (-66891825 - 40578975 z - 14836500 z^2 - 6336000 z^3 + 1650240 z^4 - 62208 z^5 + 512 z^6) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] + (97297200 + 245116125 z + 150431850 z^2 + 56638800 z^3 + 26820000 z^4 - 6661632 z^5 + 249344 z^6 - 2048 z^7) BesselI[1, Sqrt[z]]^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]