Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8970)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.8970.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, -(7/4)}, z] == ((16 z (5719161735 - 6675812640 z - 5506583040 z^2 - 8618803200 z^3 + 2364493824 z^4 - 107347968 z^5 + 1048576 z^6) BesselI[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-6230890575 - 29850599520 z - 20369422080 z^2 - 13403013120 z^3 + 4544225280 z^4 - 212860928 z^5 + 2097152 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (-93463358625 + 76236778800 z + 229491843840 z^2 + 159063367680 z^3 + 111167078400 z^4 - 36560240640 z^5 + 1704984576 z^6 - 16777216 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(53230362570 Sqrt[2] z^(5/4))

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]