Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8ra)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8ra.01

Input Form

HypergeometricPFQ[{-(13/4)}, {9/2, 21/4}, z] == (17 (2 Sqrt[z] (2798273553075 + 23342863143600 z + 21665362118400 z^2 + 34012744888320 z^3 - 21418783211520 z^4 + 1885936287744 z^5 - 44342181888 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]]^2 - 3 (4663789255125 + 35588299546800 z + 29358846316800 z^2 + 17784766771200 z^3 - 19832304107520 z^4 + 1847533240320 z^5 - 44107300864 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 2 Sqrt[z] (13991367765375 + 39471625393200 z + 30811076524800 z^2 + 19677924864000 z^3 - 20047171092480 z^4 + 1852943892480 z^5 - 44140855296 z^6 + 268435456 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(353673322168320 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]