Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9628)

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/07.22.03.9628.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, -(21/4)}, z] == ((4 z (-1328759598755964375 - 19469005109977500 z - 9385577528342400 z^2 + 6508250942054400 z^3 + 1545405714432000 z^4 + 126426745405440 z^5 + 5450791649280 z^6 + 141197049856 z^7 + 2147483648 z^8) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-3986278796267893125 - 817698214619055000 z + 161820302212800 z^2 + 3889652978534400 z^3 + 817777929830400 z^4 + 65047819714560 z^5 + 2771323453440 z^6 + 71269613568 z^7 + 1073741824 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (11958836388803679375 + 4730968241724532500 z + 348439565739711600 z^2 - 27018770459788800 z^3 + 27829446259507200 z^4 + 6317766269337600 z^5 + 511394206187520 z^6 + 21947719090176 z^7 + 566935683072 z^8 + 8589934592 z^9) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(10459477540512000 Sqrt[2] z^(15/4))

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]