Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0941)

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=5/2

http://functions.wolfram.com/07.22.03.0941.01

Input Form

HypergeometricPFQ[{-(9/2)}, {5/2, 6}, z] == (1/(20951330400 z^(9/2))) (-4 (2 Sqrt[z] (489888000 - 220449600 z + 247665600 z^2 - 914457600 z^3 - 4741835175 z^4 + 3689859060 z^5 - 493211232 z^6 + 19600512 z^7 - 262912 z^8 + 1024 z^9) BesselI[0, 2 Sqrt[z]] - (979776000 + 48988800 z + 193233600 z^2 - 1524096000 z^3 - 3252014325 z^4 + 3459264660 z^5 - 483636384 z^6 + 19469952 z^7 - 262400 z^8 + 1024 z^9) BesselI[1, 2 Sqrt[z]]) + Pi z^(7/2) (-5892561675 - 15713497800 z + 14284998000 z^2 - 1953504000 z^3 + 78140160 z^4 - 1050624 z^5 + 4096 z^6) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi z^(7/2) (5892561675 + 15713497800 z - 14284998000 z^2 + 1953504000 z^3 - 78140160 z^4 + 1050624 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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type='rational'> 1 <sep /> 2 </cn> </apply> </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]