Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7ra)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.a7ra.01

Input Form

HypergeometricPFQ[{-(17/4)}, {3/2, 21/4}, z] == ((-2 Sqrt[z] (17695362710025 - 32558367441600 z + 26147260339200 z^2 - 1004025673728000 z^3 + 1644064063488000 z^4 - 473419619500032 z^5 + 34164921335808 z^6 - 739808116736 z^7 + 4294967296 z^8) BesselI[1/4, Sqrt[z]]^2 + 3 (29492271183375 - 75236227466400 z + 50618414246400 z^2 - 87604496179200 z^3 + 1275729857740800 z^4 - 444589544570880 z^5 + 33523931021312 z^6 - 736050020352 z^7 + 4294967296 z^8) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (88476813550125 - 36958146825600 z + 44249209804800 z^2 - 150179136307200 z^3 + 1320503780966400 z^4 - 448511229296640 z^5 + 33614293106688 z^6 - 736586891264 z^7 + 4294967296 z^8) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(956797393305600 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]