Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a80o)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.a80o.01

Input Form

HypergeometricPFQ[{-(15/4)}, {-(7/2), 23/4}, z] == (19 (2 Sqrt[z] (-19996834479496875 - 17359445343240000 z + 259355416320000 z^2 - 98802063360000 z^3 + 71196268953600 z^4 + 19007432294400 z^5 + 1836098519040 z^6 + 102005473280 z^7 + 4294967296 z^8) BesselI[-(1/4), Sqrt[z]]^2 - (-59990503438490625 - 143492436507420000 z - 13995929787840000 z^2 + 29640619008000 z^3 + 88017076224000 z^4 + 20376295833600 z^5 + 1907066142720 z^6 + 104689827840 z^7 + 4294967296 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (59990503438490625 + 15512695838640000 z + 403853433984000 z^2 - 66881396736000 z^3 + 76933192089600 z^4 + 19514209075200 z^5 + 1863277608960 z^6 + 103079215104 z^7 + 4294967296 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (2242456112332800 Sqrt[2] z^(17/4))

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]