Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0609)

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

For fixed z and a₁=-11/2, b₁=3

http://functions.wolfram.com/07.22.03.0609.01

Input Form

HypergeometricPFQ[{-(11/2)}, {3, 5}, z] == (1/(442384067750625 z^3)) (64 (z (63212774625 + 1517106591000 z + 10248261685200 z^2 - 8612284111200 z^3 + 1432660003200 z^4 - 77415690240 z^5 + 1601095680 z^6 - 12853248 z^7 + 32768 z^8) BesselI[0, Sqrt[z]]^2 - 4 Sqrt[z] (63212774625 + 674269596000 z + 1398473237700 z^2 - 1913439250800 z^3 + 344293524000 z^4 - 19059056640 z^5 + 397877760 z^6 - 3207168 z^7 + 8192 z^8) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] - 4 (-63212774625 + 168567399000 z + 750761099550 z^2 + 1704439251900 z^3 - 1987355082600 z^4 + 348778542240 z^5 - 19156170240 z^6 + 398673408 z^7 - 3209216 z^8 + 8192 z^9) 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]