Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9592)

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`=9/2

http://functions.wolfram.com/07.22.03.9592.01

Input Form

HypergeometricPFQ[{-(19/4)}, {9/2, -(9/4)}, z] == ((4 z (498438430875 - 143649336600 z + 183240921600 z^2 + 125184153600 z^3 + 36666408960 z^4 + 13707509760 z^5 - 1977614336 z^6 + 33554432 z^7) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (1495315292625 - 146126049300 z + 144478857600 z^2 + 76678272000 z^3 + 21151088640 z^4 + 6263930880 z^5 - 978321408 z^6 + 16777216 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (4485945877875 + 416087733600 z + 305548135200 z^2 - 913136716800 z^3 - 546761318400 z^4 - 157530193920 z^5 - 52904853504 z^6 + 7876902912 z^7 - 134217728 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(411150168000 Sqrt[2] z^(11/4))

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]