Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9046)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.9046.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, 21/4}, z] == ((2 Sqrt[z] (1083897269415835875 + 11709796141381338000 z + 14758084952516505600 z^2 + 41595498305825587200 z^3 - 34717658726390169600 z^4 + 4990111963970273280 z^5 - 232983199418941440 z^6 + 4217734120341504 z^7 - 30034706300928 z^8 + 68719476736 z^9) BesselI[1/4, Sqrt[z]]^2 - 3 (1806495449026393125 + 18231707916327906000 z + 20734365126803328000 z^2 + 17321961939945062400 z^3 - 30669748778188800000 z^4 + 4792287557320704000 z^5 - 229336579917742080 z^6 + 4191555220930560 z^7 - 29974576758784 z^8 + 68719476736 z^9) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 2 Sqrt[z] (5419486347079179375 + 21450749305499514000 z + 22565166125838336000 z^2 + 19857784440762777600 z^3 - 31192400342709043200 z^4 + 4819437509935104000 z^5 - 229849257077637120 z^6 + 4195275736350720 z^7 - 29983166693376 z^8 + 68719476736 z^9) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (29163902145999667200 Sqrt[2] z^(15/4))

Standard Form

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MathML Form

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<cn type='rational'> 5 <sep /> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 5 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 29163902145999667200 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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]