Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0650)

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=5

http://functions.wolfram.com/07.22.03.0650.01

Input Form

HypergeometricPFQ[{-(11/2)}, {5, 6}, -z] == (512 (2 z (-387936797873625 + 461457292128525 z - 284517564962400 z^2 + 382446919839600 z^3 + 164156722329600 z^4 + 14983378099200 z^5 + 488293134336 z^6 + 6545977344 z^7 + 35979264 z^8 + 65536 z^9) BesselJ[0, Sqrt[z]]^2 - 2 Sqrt[z] (-694202690931750 + 682018774893225 z - 398956911229800 z^2 + 280407925828800 z^3 + 153681286651200 z^4 + 14627848596480 z^5 + 483443702784 z^6 + 6519103488 z^7 + 35930112 z^8 + 65536 z^9) BesselJ[0, Sqrt[z]] BesselJ[1, Sqrt[z]] + (326683619262000 - 1392355487736675 z + 1292844660896250 z^2 - 775152063100800 z^3 + 620537905864800 z^4 + 314024032465920 z^5 + 29488063223808 z^6 + 970093854720 z^7 + 13056073728 z^8 + 71892992 z^9 + 131072 z^10) BesselJ[1, Sqrt[z]]^2))/ (200046075436832625 z^4)

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]