Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8452)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.8452.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, 3/4}, z] == ((4 z (6059961975375 - 6421985677800 z + 303527027865600 z^2 - 854163192405600 z^3 + 299017713646080 z^4 - 27584960348160 z^5 + 866997501952 z^6 - 9820962816 z^7 + 33554432 z^8) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (18179885926125 - 15803121618900 z + 28206368467200 z^2 - 352471543578000 z^3 + 141562192907520 z^4 - 13529596354560 z^5 + 430457880576 z^6 - 4899995648 z^7 + 16777216 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (54539657778375 - 37020858613200 z + 75049087528800 z^2 - 676952843212800 z^3 + 3155040696931200 z^4 - 1169770765363200 z^5 + 109487942074368 z^6 - 3458221473792 z^7 + 39250296832 z^8 - 134217728 z^9) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (1171366828632000 Sqrt[2] z^(11/4))

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]