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

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`=-11/2

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

Input Form

HypergeometricPFQ[{15/4}, {-(11/2), 21/4}, z] == (221 (2 Sqrt[z] (-202408453672425 + 183112447240800 z + 52561180869120 z^2 + 5295779241984 z^3 + 264794406912 z^4 + 6348079104 z^5 + 33554432 z^6) BesselI[1/4, Sqrt[z]]^2 - 3 (-337347422787375 + 545078912716800 z + 231442236748800 z^2 + 31259005747200 z^3 + 2023145865216 z^4 + 68048388096 z^5 + 872415232 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (1012042268362125 + 523786767688800 z + 94091002790400 z^2 + 7845198520320 z^3 + 347001716736 z^4 + 7354712064 z^5 + 33554432 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(111906127872 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]