Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0575)

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=2

http://functions.wolfram.com/07.22.03.0575.01

Input Form

HypergeometricPFQ[{-(11/2)}, {2, 4}, z] == (1/(1552224799125 z^2)) (4 (z (1404728325 + 471988717200 z - 706532349600 z^2 + 195474559680 z^3 - 15940189440 z^4 + 463945728 z^5 - 4984832 z^6 + 16384 z^7) BesselI[0, Sqrt[z]]^2 - 4 Sqrt[z] (1404728325 + 39332393100 z - 145678856400 z^2 + 46063482480 z^3 - 3900119040 z^4 + 115058688 z^5 - 1243136 z^6 + 4096 z^7) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] + (5618913300 - 21070924875 z - 227256321600 z^2 + 619451831520 z^3 - 187837479360 z^4 + 15711904512 z^5 - 461465600 z^6 + 4976640 z^7 - 16384 z^8) BesselI[1, Sqrt[z]]^2))

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]