Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0995)

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=11/2

http://functions.wolfram.com/07.22.03.0995.01

Input Form

HypergeometricPFQ[{-(9/2)}, {11/2, 6}, z] == (-4 (2 Sqrt[z] (-8427641241600 - 22589952362775 z - 15627437406000 z^2 - 6883522430400 z^3 - 5737058046720 z^4 + 1952177315328 z^5 - 132020932608 z^6 + 3006873600 z^7 - 25231360 z^8 + 65536 z^9) BesselI[0, 2 Sqrt[z]] + (16855282483200 + 31952381811525 z + 19648114579800 z^2 + 8512142839200 z^3 + 4864081622400 z^4 - 1888686867456 z^5 + 130539276288 z^6 - 2994315264 z^7 + 25198592 z^8 - 65536 z^9) BesselI[1, 2 Sqrt[z]]) + Pi Sqrt[z] (-64965492466875 - 111369415657500 z - 71276426020800 z^2 - 31678411564800 z^3 - 21118941043200 z^4 + 7679614924800 z^5 - 525101875200 z^6 + 12002328576 z^7 - 100859904 z^8 + 262144 z^9) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi Sqrt[z] (64965492466875 + 111369415657500 z + 71276426020800 z^2 + 31678411564800 z^3 + 21118941043200 z^4 - 7679614924800 z^5 + 525101875200 z^6 - 12002328576 z^7 + 100859904 z^8 - 262144 z^9) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])/(17163329863680 z^(9/2))

Standard Form

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MathML Form

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<apply> <plus /> <apply> <times /> <cn type='integer'> -262144 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 100859904 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12002328576 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 525101875200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 7679614924800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 21118941043200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 31678411564800 </cn> <apply> <power 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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]