Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8805)

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/07.22.03.8805.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(1/2), 19/4}, -z] == ((-Sqrt[Pi]) (1662432759862875 + 1280162125242000 z + 900333802368000 z^2 + 1244905998336000 z^3 - 5975548792012800 z^4 + 19121756134440960 z^5 + 7554274028421120 z^6 + 569238859284480 z^7 + 12176232284160 z^8 + 68719476736 z^9) FresnelS[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) (4 Sqrt[z] (554144253287625 + 173397621196800 z + 145980048614400 z^2 - 473336352276480 z^3 + 1119376923033600 z^4 + 465772593807360 z^5 + 35436500090880 z^6 + 760209211392 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] + (-1662432759862875 + 493099485278400 z + 14820309504000 z^2 - 580956132556800 z^3 + 860958242242560 z^4 + 441455801794560 z^5 + 34879832064000 z^6 + 756987985920 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]]))/(6234230929489920 z^(15/4))

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]