Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9074)

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`=11/2

http://functions.wolfram.com/07.22.03.9074.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, 1/4}, z] == ((4 z (-8243468230725 + 3571399868400 z + 25798830220800 z^2 - 159361916313600 z^3 + 133793702138880 z^4 - 21770233970688 z^5 + 1016106319872 z^6 - 15502147584 z^7 + 67108864 z^8) BesselI[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-13739113717875 + 4731078561300 z - 2564081956800 z^2 - 34398440294400 z^3 + 58074170918400 z^4 - 10451795558400 z^5 + 501320515584 z^6 - 7721713664 z^7 + 33554432 z^8) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (-206086705768125 + 52647360129000 z - 31526840217600 z^2 + 33951981772800 z^3 + 310925338214400 z^4 - 473684566118400 z^5 + 84092847390720 z^6 - 4018183077888 z^7 + 61807263744 z^8 - 268435456 z^9) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (55359577072800 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]