Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7ur)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a7ur.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, 1/4}, -z] == ((4 z (-366522975 + 4801401360 z + 29011207680 z^2 + 23578345728 z^3 + 3393761280 z^4 + 121569280 z^5 + 1048576 z^6) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-610871625 - 392628600 z + 6335038080 z^2 + 10390719360 z^3 + 1644468224 z^4 + 60325888 z^5 + 524288 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (-9163074375 - 5074933500 z - 5814244800 z^2 + 57307944960 z^3 + 84598133760 z^4 + 13214466048 z^5 + 483131392 z^6 + 4194304 z^7) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (10139116680 Sqrt[2] z^(9/4))

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]