Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8707)

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/07.22.03.8707.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(5/2), 17/4}, -z] == -(((2 Sqrt[z] (59768253069525 + 92395367064000 z - 34466719795200 z^2 - 46741870264320 z^3 + 21695973949440 z^4 - 4534642409472 z^5 + 4227858432000 z^6 + 338228674560 z^7 + 4294967296 z^8) BesselJ[1/4, Sqrt[z]]^2 - 3 (99613755115875 + 224828726522400 z + 75213070732800 z^2 - 82031046451200 z^3 + 29999050260480 z^4 - 7762744442880 z^5 + 3938250129408 z^6 + 334470578176 z^7 + 4294967296 z^8) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (298841265347625 + 36958146825600 z + 49648036838400 z^2 - 73735358054400 z^3 + 28342712401920 z^4 - 7385540198400 z^5 + 3978414784512 z^6 + 335007449088 z^7 + 4294967296 z^8) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(77825625292800 Sqrt[2] z^(11/4)))

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]