Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8133)

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`=-5/2

http://functions.wolfram.com/07.22.03.8133.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(5/2), 19/4}, -z] == ((-2 Sqrt[z] (27393782656865625 - 16165889401662000 z - 3469540314240000 z^2 - 7969803367219200 z^3 + 5410031557017600 z^4 - 1631029926297600 z^5 + 531221352284160 z^6 + 214436979671040 z^7 + 8456790605824 z^8 + 68719476736 z^9) BesselJ[-(1/4), Sqrt[z]]^2 + (82181347970596875 - 173726388922086000 z - 24980690262528000 z^2 - 8141854604083200 z^3 + 5911404016435200 z^4 - 1690509665894400 z^5 + 410603571118080 z^6 + 209266912788480 z^7 + 8413840932864 z^8 + 68719476736 z^9) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 2 Sqrt[z] (-82181347970596875 - 1593820081854000 z - 5134919665075200 z^2 - 9109767389184000 z^3 + 5765560595251200 z^4 - 1694357205811200 z^5 + 480789040988160 z^6 + 212349625565184 z^7 + 8439610736640 z^8 + 68719476736 z^9) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(17118749786112000 Sqrt[2] z^(13/4))

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]