Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8464)

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`=9/2

http://functions.wolfram.com/07.22.03.8464.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, 15/4}, z] == ((2 z (564137993952658125 + 1216030510887192000 z + 6555317303604326400 z^2 - 3343603283564544000 z^3 + 399803447210803200 z^4 - 16852689711267840 z^5 + 285645524172800 z^6 - 1942398959616 z^7 + 4294967296 z^8) BesselI[-(1/4), Sqrt[z]]^2 - Sqrt[z] (1425259377661494375 + 2502109595077092000 z + 4979461128728486400 z^2 - 3118998847107686400 z^3 + 389728385276313600 z^4 - 16677373917265920 z^5 + 284438739025920 z^6 - 1939714605056 z^7 + 4294967296 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 (200365953147360000 + 1139424822624713625 z + 2048757772991529600 z^2 + 5849290305687628800 z^3 - 3249744475801190400 z^4 + 395698359523737600 z^5 - 16782029173555200 z^6 + 285161602154496 z^7 - 1941325217792 z^8 + 4294967296 z^9) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (8606655804764160000 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]