Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9990)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.9990.01

Input Form

HypergeometricPFQ[{-(17/4)}, {1/2, 5/4}, z] == (1/(26195400 Sqrt[2] z^(1/4))) ((-2 (-26195400 + 223627635 z - 287955360 z^2 + 76575744 z^3 - 4743168 z^4 + 65536 z^5) BesselI[1/4, Sqrt[z]]^2 + 3 Sqrt[z] (58367925 - 227525760 z + 72522240 z^2 - 4685824 z^3 + 65536 z^4) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 z (70322175 - 234995040 z + 73082880 z^2 - 4694016 z^3 + 65536 z^4) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)

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]