Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8496)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.8496.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, -(1/4)}, z] == -(((4 z (1099056740079375 - 363597718522500 z + 177388752340800 z^2 - 632732692838400 z^3 - 2591100687974400 z^4 + 2152411421368320 z^5 - 283944399667200 z^6 + 10970462158848 z^7 - 142472118272 z^8 + 536870912 z^9) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (3297170220238125 - 462760732665000 z + 291771071222400 z^2 - 328219560345600 z^3 - 807778079539200 z^4 + 995899751239680 z^5 - 138660461936640 z^6 + 5441159430144 z^7 - 71068286976 z^8 + 268435456 z^9) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (9891510660714375 + 495815070712500 z + 513003326497200 z^2 - 796738330080000 z^3 + 3200140713369600 z^4 + 8584791854284800 z^5 - 8341833603317760 z^6 + 1125025796063232 z^7 - 43740215377920 z^8 + 569351602176 z^9 - 2147483648 z^10) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(1940446059552000 Sqrt[2] z^(15/4)))

Standard Form

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MathML Form

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<ci> z </ci> <cn type='rational'> 15 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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]