Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0915)

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=2

http://functions.wolfram.com/07.22.03.0915.01

Input Form

HypergeometricPFQ[{-(9/2)}, {2, 7/2}, z] == (1/(7153090560 z^2)) (-4 (2 z (-9823275 - 1211497560 z + 1950110064 z^2 - 497233152 z^3 + 33706752 z^4 - 710656 z^5 + 4096 z^6) BesselI[0, 2 Sqrt[z]] + Sqrt[z] (29469825 + 550897200 z - 1727975088 z^2 + 480983040 z^3 - 33355008 z^4 + 708608 z^5 - 4096 z^6) BesselI[1, 2 Sqrt[z]]) + Pi (29469825 - 275051700 z - 3300620400 z^2 + 7334712000 z^3 - 1955923200 z^4 + 134120448 z^5 - 2838528 z^6 + 16384 z^7) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi (-29469825 + 275051700 z + 3300620400 z^2 - 7334712000 z^3 + 1955923200 z^4 - 134120448 z^5 + 2838528 z^6 - 16384 z^7) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 275051700 </cn> <ci> z </ci> </apply> <cn type='integer'> -29469825 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> StruveL </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> </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]