Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9071)

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`=11/2

http://functions.wolfram.com/07.22.03.9071.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, -(3/4)}, -z] == -(((4 z (19234759205025 + 5931807827400 z - 6890222102400 z^2 - 5225413939200 z^3 + 35613720576000 z^4 + 14802370265088 z^5 + 1133495451648 z^6 + 24134025216 z^7 + 134217728 z^8) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (32057932008375 + 7036752422700 z + 2917748433600 z^2 - 10208665958400 z^3 + 12093419520000 z^4 + 6922658856960 z^5 + 556288180224 z^6 + 12008292352 z^7 + 67108864 z^8) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (480868980125625 + 62807376996000 z + 32922559706400 z^2 + 27114429888000 z^3 - 81007124889600 z^4 + 102232837324800 z^5 + 55902403952640 z^6 + 4462108213248 z^7 + 96133447680 z^8 + 536870912 z^9) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(18453192357600 Sqrt[2] z^(13/4)))

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]