Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0861)

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=1/2

http://functions.wolfram.com/07.22.03.0861.01

Input Form

HypergeometricPFQ[{-(9/2)}, {1/2, 5}, z] == (1/(34459425 z^(7/2))) (2 (-4 (Sqrt[z] (-1786050 + 552825 z - 510300 z^2 - 3175200 z^3 + 19186560 z^4 - 8542998 z^5 + 775992 z^6 - 19616 z^7 + 128 z^8) BesselI[0, 2 Sqrt[z]] + (1786050 + 340200 z + 85050 z^2 - 793800 z^3 - 7755840 z^4 + 4085793 z^5 - 383148 z^6 + 9776 z^7 - 64 z^8) BesselI[1, 2 Sqrt[z]]) + Pi z^(9/2) (34459425 - 16707600 z + 1542240 z^2 - 39168 z^3 + 256 z^4) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi z^(9/2) (-34459425 + 16707600 z - 1542240 z^2 + 39168 z^3 - 256 z^4) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]]))

Standard Form

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MathML Form

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</apply> </apply> <apply> <times /> <cn type='integer'> 340200 </cn> <ci> z </ci> </apply> <cn type='integer'> 1786050 </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> </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]