Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0546)

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=1

http://functions.wolfram.com/07.22.03.0546.01

Input Form

HypergeometricPFQ[{-(11/2)}, {1, 6}, -z] == (1/(9528272228475 z^4)) (32 (2 z (31120135200 + 12642554925 z + 6483361500 z^2 + 154304003700 z^3 + 333226444320 z^4 + 104971198752 z^5 + 8779696128 z^6 + 251251200 z^7 + 2605056 z^8 + 8192 z^9) BesselJ[0, Sqrt[z]]^2 - Sqrt[z] (248961081600 + 70020304200 z + 37927664775 z^2 + 36306824400 z^3 + 534155640480 z^4 + 197570149056 z^5 + 17191141632 z^6 + 498622464 z^7 + 5197824 z^8 + 16384 z^9) BesselJ[0, Sqrt[z]] BesselJ[1, Sqrt[z]] + 2 (124480540800 + 19450084500 z + 13939227225 z^2 + 15560067600 z^3 + 45383530500 z^4 + 286620063408 z^5 + 100761968160 z^6 + 8655998976 z^7 + 249954816 z^8 + 2600960 z^9 + 8192 z^10) BesselJ[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]