Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0570)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-11/2, b_1`>=-11/2

For fixed z and a₁=-11/2, b₁=2

http://functions.wolfram.com/07.22.03.0570.01

Input Form

HypergeometricPFQ[{-(11/2)}, {2, 5/2}, -z] == (1/(116237721600 z)) (4 (2 z (17414483625 + 43375668840 z + 17966947824 z^2 + 2016673536 z^3 + 76363520 z^4 + 1026048 z^5 + 4096 z^6) BesselJ[0, 2 Sqrt[z]] - Sqrt[z] (5301294075 + 35858914560 z + 17020988208 z^2 + 1979371008 z^3 + 75854080 z^4 + 1024000 z^5 + 4096 z^6) BesselJ[1, 2 Sqrt[z]]) + Pi (-1404728325 + 39332393100 z + 157329572400 z^2 + 69924254400 z^3 + 7991343360 z^4 + 304432128 z^5 + 4100096 z^6 + 16384 z^7) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi (-1404728325 + 39332393100 z + 157329572400 z^2 + 69924254400 z^3 + 7991343360 z^4 + 304432128 z^5 + 4100096 z^6 + 16384 z^7) BesselJ[0, 2 Sqrt[z]] StruveH[1, 2 Sqrt[z]])

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]