Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7984)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.7984.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(11/2), 15/4}, z] == ((2 Sqrt[z] (-52961313136606875 - 29346528491280000 z + 26941205491200000 z^2 + 11360885708390400 z^3 + 1536575304499200 z^4 + 108852632616960 z^5 + 4882169856000 z^6 + 156766306304 z^7 + 4294967296 z^8) BesselI[-(1/4), Sqrt[z]]^2 - (-158883939409820625 - 330148445526900000 z + 39668410926144000 z^2 + 12600085994496000 z^3 + 1615302859161600 z^4 + 112217271828480 z^5 + 4987363000320 z^6 + 159450660864 z^7 + 4294967296 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (158883939409820625 - 8803958547384000 z + 30763257452928000 z^2 + 11800875018240000 z^3 + 1566064204185600 z^4 + 110142318182400 z^5 + 4923039154176 z^6 + 157840048128 z^7 + 4294967296 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (52031989481472000 Sqrt[2] z^(9/4))

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]