Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0968)

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=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=7/2

http://functions.wolfram.com/07.22.03.0968.01

Input Form

HypergeometricPFQ[{-(9/2)}, {7/2, 6}, -z] == (1/(234654900480 z^(9/2))) (4 (2 Sqrt[z] (5486745600 + 5943974400 z + 20727705600 z^2 - 31908676275 z^3 + 62758939320 z^4 + 34166644848 z^5 + 3445754112 z^6 + 109701888 z^7 + 1226752 z^8 + 4096 z^9) BesselJ[0, 2 Sqrt[z]] - (10973491200 + 6401203200 z + 34596979200 z^2 - 44516403225 z^3 + 48251926800 z^4 + 32534406576 z^5 + 3391958016 z^6 + 109092096 z^7 + 1224704 z^8 + 4096 z^9) BesselJ[1, 2 Sqrt[z]]) + Pi z^(5/2) (123743795175 - 164991726900 z + 219988969200 z^2 + 133326648000 z^3 + 13674528000 z^4 + 437584896 z^5 + 4902912 z^6 + 16384 z^7) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi z^(5/2) (123743795175 - 164991726900 z + 219988969200 z^2 + 133326648000 z^3 + 13674528000 z^4 + 437584896 z^5 + 4902912 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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1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]