Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0631)

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=4

http://functions.wolfram.com/07.22.03.0631.01

Input Form

HypergeometricPFQ[{-(11/2)}, {4, 5}, z] == (64 (z (12537200300625 + 21301829841600 z + 64920074788800 z^2 - 41305325846400 z^3 + 5393107123200 z^4 - 239003873280 z^5 + 4185808896 z^6 - 29130752 z^7 + 65536 z^8) BesselI[0, Sqrt[z]]^2 - 16 Sqrt[z] (1432822891500 + 2101605954525 z + 2567471964750 z^2 - 2351559186900 z^3 + 326289445200 z^4 - 14744563200 z^5 + 260254464 z^6 - 1817600 z^7 + 4096 z^8) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] - (4298468674500 + 24761837556225 z + 34238907133200 z^2 + 47681046705600 z^3 - 38775890707200 z^4 + 5276656327680 z^5 - 236932614144 z^6 + 4171292672 z^7 - 29097984 z^8 + 65536 z^9) BesselI[1, Sqrt[z]]^2))/(2506843050586875 z^3)

Standard Form

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MathML Form

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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]