Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0565)

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

For fixed z and a₁=-11/2, b₁=3/2

http://functions.wolfram.com/07.22.03.0565.01

Input Form

HypergeometricPFQ[{-(11/2)}, {3/2, 6}, z] == (1/(329983453800 z^(9/2))) (4 (2 Sqrt[z] (9430344000 - 2357586000 z + 1728896400 z^2 - 2514758400 z^3 + 55324684800 z^4 - 87526602135 z^5 + 21521968020 z^6 - 1513612512 z^7 + 38009472 z^8 - 355072 z^9 + 1024 z^10) BesselI[0, 2 Sqrt[z]] + (-18860688000 - 4715172000 z + 471517200 z^2 + 2514758400 z^3 - 25147584000 z^4 + 77934850245 z^5 - 20796863220 z^6 + 1494913824 z^7 - 37832832 z^8 + 354560 z^9 - 1024 z^10) BesselI[1, 2 Sqrt[z]]) + Pi z^(9/2) (-151242416325 + 329983453800 z - 84611142000 z^2 + 6016792320 z^3 - 151683840 z^4 + 1419264 z^5 - 4096 z^6) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi z^(9/2) (151242416325 - 329983453800 z + 84611142000 z^2 - 6016792320 z^3 + 151683840 z^4 - 1419264 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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</apply> <apply> <times /> <cn type='integer'> 471517200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4715172000 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -18860688000 </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> </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]