Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8914)

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`=5/2

http://functions.wolfram.com/07.22.03.8914.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, -(15/4)}, z] == (1/(47220482925 z^(1/4))) (Sqrt[2] ((47220482925 - 61018897968 z - 31962615552 z^2 - 6374043648 z^3 - 813367296 z^4 - 154140672 z^5 + 8388608 z^6) BesselI[1/4, Sqrt[z]]^2 - 96 Sqrt[z] (-1604051505 - 611685648 z - 113412096 z^2 - 14622720 z^3 - 2293760 z^4 + 131072 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (43616234025 + 94172394960 z + 37806144768 z^2 + 7110512640 z^3 + 920715264 z^4 + 147849216 z^5 - 8388608 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^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]