Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a861)

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`=1/2

http://functions.wolfram.com/07.22.03.a861.01

Input Form

HypergeometricPFQ[{-(15/4)}, {1/2, 23/4}, -z] == (19 (2 Sqrt[z] (-23283371986875 + 14191769592000 z + 3175780608000 z^2 + 564583219200 z^3 + 18594584985600 z^4 + 50459679129600 z^5 + 10392478679040 z^6 + 445602856960 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]]^2 - (-69850115960625 + 149013580716000 z + 19848628800000 z^2 + 7621873459200 z^3 + 44662888857600 z^5 + 10121191096320 z^6 + 442918502400 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (69850115960625 + 2858202547200 z^2 + 3387499315200 z^3 + 9299017728000 z^4 + 48027716812800 z^5 + 10282755686400 z^6 + 444529115136 z^7 + 4294967296 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(780855253401600 Sqrt[2] z^(17/4))

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]