Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1309)

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=-7/2, b_1`>=-11/2

For fixed z and a₁=-7/2, b₁=7/2

http://functions.wolfram.com/07.22.03.1309.01

Input Form

HypergeometricPFQ[{-(7/2)}, {7/2, 6}, z] == (1/(882161280 z^(9/2))) (4 (2 Sqrt[z] (43545600 - 39916800 z + 127008000 z^2 + 165209625 z^3 + 256091220 z^4 - 113492448 z^5 + 8613504 z^6 - 183040 z^7 + 1024 z^8) BesselI[0, 2 Sqrt[z]] - (87091200 - 36288000 z + 206841600 z^2 + 224678475 z^3 + 206104500 z^4 - 109341216 z^5 + 8522880 z^6 - 182528 z^7 + 1024 z^8) BesselI[1, 2 Sqrt[z]]) - Pi z^(5/2) (723647925 + 827026200 z + 918918000 z^2 - 445536000 z^3 + 34272000 z^4 - 731136 z^5 + 4096 z^6) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi z^(5/2) (723647925 + 827026200 z + 918918000 z^2 - 445536000 z^3 + 34272000 z^4 - 731136 z^5 + 4096 z^6) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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/> <cn type='integer'> 36288000 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 87091200 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 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]