Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8798)

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`=-1/2

http://functions.wolfram.com/07.22.03.8798.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(1/2), 13/4}, z] == ((2 Sqrt[z] (167162670675 + 4601152155600 z + 9282532089600 z^2 - 39644514201600 z^3 + 16673513472000 z^4 - 1531475656704 z^5 + 39812333568 z^6 - 268435456 z^7) BesselI[1/4, Sqrt[z]]^2 + 3 (-278604451125 + 1053631378800 z + 8348532192000 z^2 + 27074944512000 z^3 - 15390498816000 z^4 + 1497036226560 z^5 - 39577452544 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (-835813353375 + 1377825649200 z + 7798824633600 z^2 + 28533380198400 z^3 - 15563287756800 z^4 + 1501880647680 z^5 - 39611006976 z^6 + 268435456 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(5114459750400 Sqrt[2] z^(7/4))

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]