Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9668)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9668.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, 19/4}, z] == -(((2 z (-258189709968815625 - 320270940809820000 z - 216498309944716800 z^2 - 445887577702195200 z^3 + 122117356191744000 z^4 - 8067604461649920 z^5 + 186343028162560 z^6 - 1604707155968 z^7 + 4294967296 z^8) BesselI[-(1/4), Sqrt[z]]^2 + Sqrt[z] (611953283873806875 + 561411849398400000 z + 359850664754380800 z^2 + 381183253497446400 z^3 - 117370103847321600 z^4 + 7953785510952960 z^5 - 185347300392960 z^6 + 1602022801408 z^7 - 4294967296 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 (121961884524480000 + 433434297764593125 z + 425671175777047200 z^2 + 292135629680294400 z^3 + 418195121683046400 z^4 - 120170371409510400 z^5 + 8021637637079040 z^6 - 185943529095168 z^7 + 1603633414144 z^8 - 4294967296 z^9) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (510024047689728000 Sqrt[2] z^(15/4)))

Standard Form

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MathML Form

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</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]