Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7we)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a7we.01

Input Form

HypergeometricPFQ[{-(17/4)}, {11/2, 13/4}, z] == ((2 z (451556305200 + 9000491675175 z + 48465489552480 z^2 - 44354532499200 z^3 + 6582186885120 z^4 - 283553234944 z^5 + 4066377728 z^6 - 16777216 z^7) BesselI[1/4, Sqrt[z]]^2 + 3 Sqrt[z] (-1505187684000 - 13796669311425 z - 17784371404800 z^2 + 38988365095680 z^3 - 6339972136960 z^4 + 280019927040 z^5 - 4051697664 z^6 + 16777216 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 (2822226907500 - 4515563052000 z - 16102854843075 z^2 - 20915676381600 z^3 + 39685161035520 z^4 - 6373474222080 z^5 + 280519966720 z^6 - 4053794816 z^7 + 16777216 z^8) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(36086242832640 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]