Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.2017)

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=-3/2, b_1`>=-11/2

For fixed z and a₁=-3/2, b₁=5

http://functions.wolfram.com/07.22.03.2017.01

Input Form

HypergeometricPFQ[{-(3/2)}, {5, 6}, z] == (1/(31216185 z^4)) (512 (2 z (1029105 + 635391 z + 195552 z^2 + 90000 z^3 - 13824 z^4 + 256 z^5) BesselI[0, Sqrt[z]]^2 - 2 Sqrt[z] (1683990 + 826389 z + 242316 z^2 + 80064 z^3 - 13632 z^4 + 256 z^5) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] - (1496880 + 2993787 z + 1530702 z^2 + 461952 z^3 + 166560 z^4 - 27392 z^5 + 512 z^6) 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]