Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8b5)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8b5.01

Input Form

HypergeometricPFQ[{-(15/4)}, {9/2, 15/4}, -z] == ((2 z (1024387489125 - 1622722701600 z + 5663014905600 z^2 + 1952566886400 z^3 + 140595363840 z^4 + 2967470080 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^2 - Sqrt[z] (2473811715375 - 3112342833600 z + 4646914272000 z^2 + 1869484032000 z^3 + 138768875520 z^4 + 2956984320 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 (-449513064000 + 1841513699025 z - 2484775893600 z^2 + 5224643424000 z^3 + 1918546329600 z^4 + 139860049920 z^5 + 2963275776 z^6 + 16777216 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(6910645248000 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]